Primitive polynomials having w(x) of degree ⌊(m+1)/2⌋ and weight as low as possible

Below tables of binary primitive polynomials of degree m are given which have polynomials w(x) of lowest possible degree which is m/2 for even m and (m+1)/2 for odd m. The primitive polynomials of the table are given in hexadecimal form. For m=8 no such polynomial exists.

m p(x) w(x)
2 0x7 x + 1
3 0xb x 2 + x
4 0x13 x 2 + 1
5 0x29 x 3 + x 2
6 0x43 x 3 + 1
7 0x83 x 4 + x
8 - -
9 0x221 x 5 + x 3
10 0x543 x 5 + x 4 + x 3 + 1
11 0xa01 x 6 + x 5
12 0x1053 x 6 + x 3 + x 2 + 1
13 0x3ffd x 7 + x + 1
14 0x4053 x 7 + x 3 + x 2 + 1
15 0x8003 x 8 + x
16 0x10053 x 8 + x 3 + x 2 + 1
17 0x20009 x 9 + x 2
18 0x40107 x 9 + x 4 + x + 1
19 0xfc001 x 10 + x 7 + 1
20 0x100053 x 10 + x 3 + x 2 + 1
21 0x280001 x 11 + x 10
22 0x400003 x 11 + 1
23 0x800021 x 12 + x 3
24 0x1000443 x 12 + x 5 + x 3 + 1
25 0x2000009 x 13 + x 2
26 0x4000047 x 13 + x 3 + x + 1
27 0x8000229 x 14 + x 5 + x 3 + x 2
28 0x10000053 x 14 + x 3 + x 2 + 1
29 0x28000001 x 15 + x 14
30 0x40000053 x 15 + x 3 + x 2 + 1
31 0x80000009 x 16 + x 2
32 0x100004043 x 16 + x 7 + x 3 + 1
33 0x200002001 x 17 + x 7
34 0x400001403 x 17 + x 6 + x 5 + 1
35 0xa00000001 x 18 + x 17
36 0x1000000443 x 18 + x 5 + x 3 + 1
37 0x3f00000001 x 19 + x 16 + 1
38 0x4000000143 x 19 + x 4 + x 3 + 1
39 0x8002000001 x 20 + x 13
40 0x10000044003 x 20 + x 9 + x 7 + 1
41 0x20000000009 x 21 + x 2
42 0x40000011003 x 21 + x 8 + x 6 + 1
43 0xfffc0000001 x 22 + x 15 + 1
44 0x100000004403 x 22 + x 7 + x 5 + 1
45 0x2000000800a1 x 23 + x 10 + x 4 + x 3
46 0x400000000443 x 23 + x 5 + x 3 + 1
47 0x800000000021 x 24 + x 3
48 0x1000000045403 x 24 + x9 + x7 + x6 + x5 + 1
49 0x2000000000201 x 25 + x 5
50 0x4000000010007 x 25 + x 8 + x + 1
51 0x8000000020023 x 26 + x 9 + x 3 + x
52 0x10000000001007 x 26 + x 6 + x + 1
53 0x200000000a8001 x 27 + x 10 + x 9 + x 8
54 0x40000000000503 x 27 + x 5 + x 4 + 1
55 0x80000080000001 x 28 + x 16
56 0x100000000404003 x 28 + x 11 + x 7 + 1
57 0x200000000000081 x 29 + x 4
58 0x400000000100043 x 29 + x 10 + x 3 + 1
59 0x800000000228001 x 30 + x 11 + x 9 + x 8
60 0x1000000000000003 x 30 + 1
61 0x3f00000000000001 x 31 + x 28 + 1
62 0x4000000000004403 x 31 + x 7 + x 5 + 1
63 0x8000000000000003 x 32 + x
64 0x10000000410000003 x 32 + x 17 + x 14 + 1
65 0x20000000200000001 x 33 + x 17
66 0x40000000000100007 x 33 + x 10 + x + 1
67 0x80000000002020021 x 34 + x 13 + x 9 + x 3
68 0x100000000000000407 x 34 + x 5 + x + 1
69 0x200000000000800209 x 35 + x 12 + x 5 + x 2
70 0x400000000000140003 x 35 + x 10 + x 9 + 1
71 0x800000000000000201 x 36 + x 5
72 0x1000400000000040003 x 36 + x 29 + x 9 + 1
73 0x2000000000002000001 x 37 + x 13
74 0x4000000000000400007 x 37 + x 11 + x + 1
75 0x8000000000002022001 x 38 + x 13 + x 9 + x 7
76 0x10000000000000001403 x 38 + x 6 + x 5 + 1
77 0x20000000008000080003 x 39 + x 20 + x 10 + x
78 0x40000000000000004103 x 39 + x 7 + x 4 + 1
79 0x80000000000000000201 x 40 + x 5
80 0x100000001004000000003 x 40 + x 24 + x 19 + 1
81 0x200000000000800000001 x 41 + x 18
82 0x400000000000100000007 x 41 + x 16 + x + 1
83 0x800000000000022000009 x 42 + x 15 + x 13 + x 2
84 0x1000000000000000040043 x 42 + x 9 + x 3 + 1
85 0x3ffffffffffffffffffffd x 43 + x + 1
86 0x4000000000000000000443 x 43 + x 5 + x 3 + 1
87 0x8000000000000000002001 x 44 + x 7
88 0x10000000000000040100003 x 44 + x 15 + x 10 + 1
89 0x20000000008000000000001 x 45 + x 26
90 0x40000000000000004000007 x 45 + x 13 + x + 1
91 0xffffc000000000000000001 x 46 + x 37 + 1
92 0x100000000000000000040007 x 46 + x 9 + x + 1
93 0x280000000000000000000001 x 47 + x 46
94 0x400000000000000000000143 x 47 + x 4 + x 3 + 1
95 0x800000000000000000000801 x 48 + x 6
96 0x1000000000000000440000003 x 48 + x 17 + x 15 + 1
97 0x2000000000000000200000001 x 49 + x 17
98 0x4000000000000001000000007 x 49 + x 18 + x + 1
99 0x8000000000000000200000281 x 50 + x 17 + x 5 + x 4
100 0x10000000000000000000040013 x 50 + x 9 + x 2 + 1
101 0x20000000000000000880000009 x 51 + x 18 + x 16 + x 2
102 0x40000000000000000000010013 x 51 + x 8 + x 2 + 1
103 0x80000000000000000000000201 x 52 + x 5
104 0x100000000400000000000000103 x 52 + x 35 + x 4 + 1
105 0x200000000000000000000020001 x 53 + x 9
106 0x400000000000000001000040003 x 53 + x 18 + x 9 + 1
107 0x800000000000000002200800001 x 54 + x 19 + x 17 + x 12
108 0x1000000000000000000000011003 x 54 + x 8 + x 6 + 1
109 0x20000000000000000a0000800001 x 55 + x 22 + x 21 + x 12
110 0x4000000000000000000000000053 x 55 + x 3 + x 2 + 1
111 0x8000000000000002000000000001 x 56 + x 25
112 0x10000040000000000000000000043 x 56 + x 45 + x 3 + 1
113 0x20000000000000000000000000201 x 57 + x 5
114 0x40000000000000000000000004007 x 57 + x 7 + x + 1
115 0x80000000000000000020200000801 x 58 + x 21 + x 17 + x 6
116 0x100000000000000000000000404003 x 58 + x 11 + x 7 + 1
117 0x3ffff0000000000000000000000001 x 59 + x 50 + 1
118 0x400000000000000000000000001403 x 59 + x 6 + x 5 + 1
119 0x800000000200000000000000000001 x 60 + x 41
120 0x1000000004000000004000000000003 x 60 + x 43 + x 25 + 1
121 0x2000080000000000000000000000001 x 61 + x 52
122 0x4000000000000000000000000000047 x 61 + x 3 + x + 1
123 0xa000000000000000000000000000001 x 62 + x 61
124 0x10000000000000000000000000001007 x 62 + x 6 + x + 1
125 0x20000000000000000000088000000021 x 63 + x 22 + x 20 + x 3
126 0x40000000000000000000000000004103 x 63 + x 7 + x 4 + 1
127 0x80000000000000000000000000000003 x 64 + x
128 0x100000000000044000000000000000003 x 64 + x 39 + x 37 + 1
129 0x200000000000000000000000000000021 x 65 + x 3
130 0x400000000000000000000100004000003 x 65 + x 22 + x 13 + 1
131 0x800000000000000000000220000000201 x 66 + x 23 + x 21 + x 5
132 0x1000000000000000000000000000010007 x 66 + x 8 + x + 1
133 0x3fff000000000000000000000000000001 x 67 + x 60 + 1
134 0x4000000000000000000000000000000113 x 67 + x 4 + x 2 + 1
135 0x8000000000000000000000000000000801 x 68 + x 6
136 0x10000000000000000000000401000000003 x 68 + x 23 + x 18 + 1
137 0x20000000000000000000000000000200001 x 69 + x 11
138 0x40000000000000000000000000000400007 x 69 + x 11 + x + 1
139 0x80000000000000000000020000202000001 x 70 + x 27 + x 17 + x 13
140 0x100000000000000000000000000000000113 x 70 + x 4 + x 2 + 1
141 0x200000000000000000000000800000080801 x 71 + x 24 + x 10 + x 6
142 0x400000000000000000000000000000040043 x 71 + x 9 + x 3 + 1
143 0xffffc0000000000000000000000000000001 x 72 + x 63 + 1
144 0x1000000000000014000000000000000000003 x 72 + x 44 + x 43 + 1
145 0x2000000000000000000200000000000000001 x 73 + x 35
146 0x4000000000000000000000000000400000007 x 73 + x 17 + x + 1
147 0xfc00000000000000000000000000000000001 x 74 + x 71 + 1
148 0x10000000000000000000000000000001000013 x 74 + x 12 + x 2 + 1
149 0x20000000000000000000000008800000000201 x 75 + x 26 + x 24 + x 5
150 0x40000000000000000000000000000100400003 x 75 + x 16 + x 11 + 1
151 0x80000000000000000000000000000000000009 x 76 + x 2
152 0x100000000000000000000000040400000000107 x76 + x27 + x23 + x4 + x + 1
153 0x200000000000000000000000000000000000003 x 77 + x
154 0x400000000000000000000000040000000000007 x 77 + x 27 + x + 1
155 0xffc000000000000000000000000000000000001 x 78 + x 73 + 1
156 0x1000000000000000000000000000000000001013 x 78 + x 6 + x 2 + 1
157 0x2000000000000000000000000080800000000801 x 79 + x 28 + x 24 + x 6
158 0x4000000000000000000000000000000000110003 x 79 + x 10 + x 8 + 1
159 0x8000000000000000000000000000000080000001 x 80 + x 16
160 0x10000000000000000000000000040001000000003 x 80 + x 27 + x 18 + 1
161 0x20000000000000000000000000000008000000001 x 81 + x 20
162 0x40000000000000000000000000400000000000007 x 81 + x 29 + x + 1
163 0x80000000000000000000000000202000020000001 x 82 + x 29 + x 25 + x 15
164 0x100000000000000000000000000000000000101003 x 82 + x 10 + x 6 + 1
165 0x3fffffff0000000000000000000000000000000001 x 83 + x 68 + 1
166 0x400000000000000000000000000000000001010003 x 83 + x 12 + x 8 + 1
167 0x800000000000000000000000000000000800000001 x 84 + x 18
168 0x1000000000000000000000040000000400000000003 x 84 + x 39 + x 23 + 1
169 0x2000000000000000000000000000200000000000001 x 85 + x 29
170 0x4000000000000000000000000000000000000040007 x 85 + x 9 + x + 1
171 0xfc00000000000000000000000000000000000000001 x 86 + x 83 + 1
172 0x10000000000000000000000000000000000040000013 x 86 + x 15 + x 2 + 1
173 0x20000000000000000000000000000880000000000003 x 87 + x 30 + x 28 + x
174 0x40000000000000000000000000000000000000404003 x 87 + x 11 + x 7 + 1
175 0x80000000000000000000000000000200000000000001 x 88 + x 29
176 0x100000000000000000000000000004040000000000003 x 88 + x 31 + x 27 + 1
177 0x200000000000000000000020000000000000000000001 x 89 + x 45
178 0x400000000000000000000000000000000000000040007 x 89 + x 9 + x + 1
179 0x800000000000000000000000000002200020000000001 x 90 + x 31 + x 29 + x 21
180 0x1000000000000000000000000000000000000000014003 x 90 + x 8 + x 7 + 1
181 0x2000000000000000000000000000008080000008000001 x 91 + x 32 + x 28 + x 14
182 0x4000000000000000000000000000000000000000000143 x 91 + x 4 + x 3 + 1
183 0x8000000000000080000000000000000000000000000001 x 92 + x 64
184 0x10000000040000000400000000000000000000000000003 x 92 + x 75 + x 59 + 1
185 0x20000000000000000000000000000000000020000000001 x 93 + x 21
186 0x40000000000000000010000000000000000000000000013 x 93 + x 56 + x 2 + 1
187 0x80000000000000000000000000000022000000200000001 x 94 + x 33 + x 31 + x 17
188 0x100000000000000000000000000000000000000400040003 x 94 + x 17 + x 9 + 1
189 0x200000000000000000000000000000008000000000002003 x 95 + x 32 + x 7 + x
190 0x400000000000000000000000000000000000000140000003 x 95 + x 16 + x 15 + 1
191 0x800000000000000000000000000000000000000000000201 x 96 + x 5
192 0x1000000000000010000000040000000000000000000000003 x 96 + x 68 + x 51 + 1
193 0x2000000000000000000000000000000000000000000008001 x 97 + x 8
194 0x4000000000000000000000000000000000000000000001007 x 97 + x 6 + x + 1
195 0x80000000000000000000000000000000200000000000000a1 x 98 + x 33 + x 4 + x 3
196 0x10000000000000000000000000000000000000000040000403 x 98 + x 15 + x 5 + 1
197 0x20000000000000000000000000000000088000000020000001 x 99 + x 34 + x 32 + x 15
198 0x40000000000000000000000000000000000000000010000403 x 99 + x 14 + x 5 + 1
199 0x80000000000000000000000000000000080000000000000001 x 100 + x 34
200 0x100000000400000000000000000004000000000000000000003 x 100 + x 83 + x 43 + 1
201 0x200000000000000000000000000000000000000000000020001 x 101 + x 9
202 0x400000000000000000000000000000000000040000000000007 x 101 + x 27 + x + 1
203 0x800000000000000000000000000000000220000000000000021 x 102 + x 35 + x 33 + x 3
204 0x1000000000000000000000000000000000000000000000010013 x 102 + x 8 + x 2 + 1
205 0x3ff0000000000000000000000000000000000000000000000001 x 103 + x 98 + 1
206 0x4000000000000000000000000000000000000000000001010003 x 103 + x 12 + x 8 + 1
207 0x8000000000000000000000000000000000000000080000000001 x 104 + x 22
208 0x10000000000000000000000000000000000400000000000400003 x 104 + x 35 + x 11 + 1
209 0x20000000000000000000000000000000000000000200000000001 x 105 + x 23
210 0x40000000000000000000000100000000004000000000000000003 x 105 + x 58 + x 37 + 1
211 0x80000000000000000000000000000000002200000000800000001 x 106 + x 37 + x 35 + x 18
212 0x100000000000000000000000000000000000000000000000404003 x 106 + x 11 + x 7 + 1
213 0x200000000000000000000000000000000000800000000000000809 x 107 + x 36 + x 6 + x 2
214 0x400000000000000000000000000000000000000000000000004103 x 107 + x 7 + x 4 + 1
215 0x800000000000000000000000000000000000000000000000800001 x 108 + x 12
216 0x1000000004000000000000400000000000000000000000000000003 x 108 + x 91 + x 65 + 1
217 0x2000000000000000000000000000000000000000000200000000001 x 109 + x 23
218 0x4000000000000000000000000000000000000000000000000001007 x 109 + x 6 + x + 1
219 0x8000000000000000000000000000000000002000000000000800021 x 110 + x 37 + x 12 + x 3
220 0x10000000000000000000000000000000000000000000000000010043 x 110 + x 8 + x 3 + 1
221 0x20000000000000000000000000000000000008800000000000000081 x 111 + x 38 + x 36 + x 4
222 0x40000000000000000000000000000000000000000000000004000013 x 111 + x 13 + x 2 + 1
223 0x80000000000000000000000000000000000000000000000200000001 x 112 + x 17
224 0x100000000000000000000000000000000000044000000000000000003 x 112 + x 39 + x 37 + 1
225 0x200000000000000000000000000000002000000000000000000000001 x 113 + x 49
226 0x400000000000000000000000000000000100000000000000000000007 x 113 + x 46 + x + 1
227 0x800000000000000000000000000000000000022000000000000008001 x 114 + x 39 + x 37 + x 8
228 0x1000000000000000000000000000000000000000000000000004010003 x 114 + x 13 + x 8 + 1
229 0x2000000000000000000000000000000000000088000000000000000201 x 115 + x 40 + x 38 + x 5
230 0x4000000000000000000000000000000000000000000000014000000003 x 115 + x 20 + x 19 + 1
231 0x8000000020000000000000000000000000000000000000000000000001 x 116 + x 99
232 0x10000000000000000000000000000000000100040000000000000000003 x 116 + x 46 + x 39 + 1
233 0x20000000000000000008000000000000000000000000000000000000001 x 117 + x 80
234 0x40000000000000000000000000010000000000000000000000000000007 x 117 + x 62 + x + 1
235 0x80000000000000000000000000000000000000220000000000002000001 x 118 + x 41 + x 39 + x 13
236 0x100000000000000000000000000000000000000000000000000000100013 x 118 + x 10 + x 2 + 1
237 0x200000000000000000000000000000000000000080000000000000020081 x 119 + x 40 + x 9 + x 4
238 0x400000000000000000000000000000000000000000000000000000400043 x 119 + x 11 + x 3 + 1
239 0x800000000000000000000000000000000000000200000000000000000001 x 120 + x 41
240 0x1000000000000000040400000000000000000000000000000000000000003 x 120 + x 87 + x 83 + 1
241 0x2000000000000000008000000000000000000000000000000000000000001 x 121 + x 86
242 0x4000000000000000000001000000000000100000000000000000000000003 x 121 + x 78 + x 52 + 1
243 0xffffffffffffffffffffffffffffffffffffffffc00000000000000000001 x 122 + x 41 + 1
244 0x10000000000000000000000000000000000000000000000000000400000043 x 122 + x 17 + x 3 + 1
245 0x20000000000000000000000000000000000000000880000008000000000001 x 123 + x 42 + x 40 + x 26
246 0x40000000000000000000000000000000000000000000000000000000100103 x 123 + x 10 + x 4 + 1
247 0x80000000000000000000000002000000000000000000000000000000000001 x 124 + x 73
248 0x100000000000040000000000000000000000100000000000000000000000003 x 124 + x 99 + x 52 + 1
249 0x200000000000000000000080000000000000000000000000000000000000001 x 125 + x 82
250 0x400000000000000000000000000000000000000001000000000000000040003 x 125 + x 42 + x 9 + 1
251 0x800000000000000000000000000000000000000020200000000000000000009 x 126 + x 45 + x 41 + x 2
252 0x1000000000000000000000000000000000000000000000000000400000400003 x 126 + x 23 + x 11 + 1
253 0x3f00000000000000000000000000000000000000000000000000000000000001 x 127 + x 124 + 1
254 0x4000000000000000000000000000000000000000000000000000000500000003 x 127 + x 17 + x 16 + 1
255 0x8000000000000000000020000000000000000000000000000000000000000001 x 128 + x 87
256 0x10000000000000000000000000000000000000000004000000000000000000103 x 128 + x 43 + x 4 + 1
257 0x20000000000000000000000000000000000000000000000000000020000000001 x 129 + x 21
258 0x40000000000000000000000000000000000000000000000000000000004000007 x 129 + x 13 + x + 1
259 0x80000000000000000000000000000000000000000022000000000000000000201 x 130 + x 45 + x 43 + x 5
260 0x100000000000000000000000000000000000000000000000000040000000004003 x 130 + x 27 + x 7 + 1
261 0x200000000000000000000000000000000000000000008000000000000000000221 x 131 + x 44 + x 5 + x 3
262 0x400000000000000000000000000000000000000000000000000000000000400043 x 131 + x 11 + x 3 + 1
263 0x800000000000000000000000000000000000000000200000000000000000000001 x 132 + x 47
264 0x1000000000000000000000000000000100400000000000000000000000000000003 x 132 + x 70 + x 65 + 1
265 0x2000000000000000000000000000000000080000000000000000000000000000001 x 133 + x 64
266 0x4000000000000000000000000000000000000010000000000000000100000000003 x 133 + x 56 + x 22 + 1
267 0x8000000000000000000000000000000000000000000020000000000000000002021 x 134 + x 45 + x 7 + x 3
268 0x10000000000000000000000000000000000000000000000000000000000000000413 x 134 + x 5 + x 2 + 1
269 0x20000000000000000000000000000000000000000000088000002000000000000001 x 135 + x 46 + x 44 + x 31
270 0x40000000000000000000000000000000000000000000000000000000000100000013 x 135 + x 16 + x 2 + 1
271 0x80000000000000000200000000000000000000000000000000000000000000000001 x 136 + x 101
272 0x100000000000000000000000000000000000000004000000400000000000000000003 x 136 + x 55 + x 41 + 1
273 0x200000000000000000000000000000000000000000000000000000000000000800001 x 137 + x 12
274 0x400000000000000000000000000000000000000000000000000000040000000000007 x 137 + x 27 + x + 1
275 0x800000000000000000000000000000000000000000002000200000000000000000021 x 138 + x 49 + x 41 + x 3
276 0x1000000000000000000000000000000000000000000000000000000000000010000007 x 138 + x 14 + x + 1
277 0x3fffffffffff0000000000000000000000000000000000000000000000000000000001 x 139 + x 116 + 1
278 0x4000000000000000000000000000000000000000000000000000000000000010040003 x 139 + x 14 + x 9 + 1
279 0x8000000000000000000000000000000000000000000000000000000000000000000021 x 140 + x 3
280 0x10000000000000000000000440000000000000000000000000000000000000000000003 x 140 + x 95 + x 93 + 1
281 0x20000000000000000000000000000000000000000000000200000000000000000000001 x 141 + x 47
282 0x40000000000000000000000000000000000000000000000000000000000400000000007 x 141 + x 23 + x + 1
283 0x80000000000000000000000000000000000000000000002028000000000000000000001 x 142 + x 49 + x 45 + x 44
284 0x100000000000000000000000000000000000000000000000000000000000000000040013 x 142 + x 9 + x 2 + 1
285 0x200000000000000000000000000000000000000000000000800000000000020000000003 x 143 + x 48 + x 21 + x
286 0x400000000000000000000000000000000000000000000000000000000000000000040043 x 143 + x 9 + x 3 + 1
287 0x800000000000000000000000000000000000000000000000000000800000000000000001 x 144 + x 36
288 0x1000000000000000000004000000000000000000000100000000000000000000000000003 x 144 + x 103 + x 58 + 1
289 0x2000000000000000000000000000000000000000000000000000000000000000000200001 x 145 + x 11
290 0x4000000000000000000400000000000000000000000000000000000000000000000000007 x 145 + x 107 + x + 1
291 0x8000000000000000000000000000000000000000000000002000000000000000000280001 x 146 + x 49 + x 11 + x 10
292 0x10000000000000000000000000000000000000000000000000000000000000000401000003 x 146 + x 17 + x 12 + 1
293 0x20000000000000000000000000000000000000000000000008800000000000000000000021 x 147 + x 50 + x 48 + x 3
294 0x40000000000000000000000000000000000000000000000000000000000000000000500003 x 147 + x 11 + x 10 + 1
295 0x80000000000000000000000000000000000000000008000000000000000000000000000001 x 148 + x 62
296 0x100000000000000000000000000000000000004000000000000000000000000000000000043 x 148 + x 73 + x 3 + 1
297 0x200000000000000000000000000000000000000000000000000000000000000000000000021 x 149 + x 3
298 0x400000000000000000000000000000000000000000000000000000040000000000000000007 x 149 + x 39 + x + 1
299 0xfffffffffffc000000000000000000000000000000000000000000000000000000000000001 x 150 + x 127 + 1
300 0x1000000000000000000000000000000000000000000000000000000000000000001000000403 x 150 + x 18 + x 5 + 1
301 0x2000000000000000000000000000000000000000000000000080800000000000800000000001 x 151 + x 52 + x 48 + x 24
302 0x4000000000000000000000000000000000000000000000000000000000000000000000050003 x 151 + x 9 + x 8 + 1
303 0xfff0000000000000000000000000000000000000000000000000000000000000000000000001 x 152 + x 146 + 1
304 0x10000000000000000000400000000001000000000000000000000000000000000000000000003 x 152 + x 113 + x 90 + 1
305 0x20000000000000000000000000800000000000000000000000000000000000000000000000001 x 153 + x 102
306 0x40000000000000000000000000000000000000000000000000400000000000000000000000007 x 153 + x 53 + x + 1
307 0x80000000000000000000000000000000000000000000000000202000000000200000000000001 x 154 + x 53 + x 49 + x 29
308 0x100000000000000000000000000000000000000000000000000000000000000000000100000043 x 154 + x 16 + x 3 + 1
309 0x200000000000000000000000000000000000000000000000000080000000000000000000280001 x 155 + x 52 + x 11 + x 10
310 0x400000000000000000000000000000000000000000000000000000000000000000000010000403 x 155 + x 14 + x 5 + 1
311 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc000001 x 156 + x 13 + 1
312 0x1000000000000000400040000000000000000000000000000000000000000000000000000000003 x 156 + x 125 + x 117 + 1
313 0x2000000000000000000000000000000000000000000000000000000000080000000000000000001 x 157 + x 40
314 0x4000000000000000000000000000000000000000000000000000000000000040000000000000007 x 157 + x 33 + x + 1
315 0x8000000000000000000000000000000000000000000000000000200000000000000000000008003 x 158 + x 53 + x 8 + x
316 0x10000000000000000000000000000000000000000000000000000000000000000000000000100103 x 158 + x 10 + x 4 + 1
317 0x20000000000000000000000000000000000000000000000000000880000000000000200000000001 x 159 + x 54 + x 52 + x 23
318 0x40000000000000000000000000000000000000000000000000000000000000000000000000011003 x 159 + x 8 + x 6 + 1
319 0x80000000000000000000000000000000000000000000000200000000000000000000000000000001 x 160 + x 65
320 0x100000000000000000000000000404000000000000000000000000000000000000000000000000003 x 160 + x 107 + x 103 + 1
321 0x200000000000000000000000000000000000000000000000000000000000000000000000080000001 x 161 + x 16
322 0x400000000000000000000000000000000000000000000000000000000000000000000000004000007 x 161 + x 13 + x + 1
323 0x800000000000000000000000000000000000000000000000000002200000000000020000000000001 x 162 + x 55 + x 53 + x 27
324 0x1000000000000000000000000000000000000000000000000000000000000000000000000000000017 x 162 + x 2 + x + 1
325 0x2000000000000000000000000000000000000000000000000000008080000008000000000000000001 x 163 + x 56 + x 52 + x 38
326 0x4000000000000000000000000000000000000000000000000000000000000000000000000100010003 x 163 + x 16 + x 8 + 1
327 0x8000000000000000000000000000000000000080000000000000000000000000000000000000000001 x 164 + x 88
328 0x10000000040000000000000000001000000000000000000000000000000000000000000000000000003 x 164 + x 147 + x 108 + 1
329 0x20000000000000800000000000000000000000000000000000000000000000000000000000000000001 x 165 + x 138
330 0x40000000000000000000000000000000000000000000000000000000000000004000000000000000007 x 165 + x 37 + x + 1
331 0x80000000000000000000000000000000000000000000000000000020200000000800000000000000001 x 166 + x 57 + x 53 + x 36
332 0x100000000000000000000000000000000000000000000000000000000000000000000000000000000047 x 166 + x 3 + x + 1
333 0x280000000000000000000000000000000000000000000000000000000000000000000000000000000001 x 167 + x 166
334 0x400000000000000000000000000000000000000000000000000000000000000000000000000000044003 x 167 + x 9 + x 7 + 1
335 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000a003 x 168 + x 8 + x 7 + x
336 0x1000000000000000000000000000000000000000000000040000000000000400000000000000000000003 x 168 + x 75 + x 47 + 1
337 0x2000000000000000000000000000000000000000000000000000000000000000000000080000000000001 x 169 + x 28
338 0x4000000000000000000000000000000000000000000000010000000000000000000000000000000000007 x 169 + x 74 + x + 1
339 0x8000000000000000000000000000000000000000000000000000000020000000000000000000082000001 x 170 + x 57 + x 16 + x 13
340 0x10000000000000000000000000000000000000000000000000000000000000000000000000000000004043 x 170 + x 7 + x 3 + 1
341 0x20000000000000000000000000000000000000000000000000000000800080000000000000000000000009 x 171 + x 60 + x 52 + x 2
342 0x40000000000000000000000000000000000000000000000000000000000000000000000000000000040043 x 171 + x 9 + x 3 + 1
343 0x80000000000000000000000000000000000000000000000000000000000000000008000000000000000001 x 172 + x 38
344 0x100000000000000000000000040000000000000000000000000000000000000000010000000000000000003 x 172 + x 123 + x 38 + 1
345 0x200000000000000000000000000000000000000000000000000000000000000000000000000002000000001 x 173 + x 19
346 0x400000000000000000000000000000000000000000000000000000000000040000000000000000000000007 x 173 + x 51 + x + 1
347 0x800000000000000000000000000000000000000000000000000000000220000000000200000000000000001 x 174 + x 59 + x 57 + x 35
348 0x1000000000000000000000000000000000000000000000000000000000000000000000000000000000040403 x 174 + x 9 + x 5 + 1
349 0x2000000000000000000000000000000000000000000000000000000000808000000000000020000000000001 x 175 + x 60 + x 56 + x 27
350 0x4000000000000000000000000000000000000000000000000000000000000000000000000000000010000043 x 175 + x 14 + x 3 + 1
351 0x8000000000000000000000000000000000000000000000000000000000000000000000000080000000000001 x 176 + x 28
352 0x10000000000000000000000000000001000000000000000000000000000400000000000000000000000000003 x 176 + x 114 + x 59 + 1
353 0x20000000000000000000000000000000000000000000000000000000000000000000000200000000000000001 x 177 + x 35
354 0x40000000000000000000000000000000000000000000000001000000000000010000000000000000000000003 x 177 + x 78 + x 50 + 1
355 0x80000000000000000000000000000000000000000000000000000000002200000000000000008000000000001 x 178 + x 61 + x 59 + x 26
356 0x100000000000000000000000000000000000000000000000000000000000000000000000000000000000001013 x 178 + x 6 + x 2 + 1
357 0x3fffffffffffffffffffffffff0000000000000000000000000000000000000000000000000000000000000001 x 179 + x 128 + 1
358 0x400000000000000000000000000000000000000000000000000000000000000000000000000000000001000013 x 179 + x 12 + x 2 + 1
359 0x800000000000000000000000000000000000000000000000000000000000200000000000000000000000000001 x 180 + x 59
360 0x1000000000000000000000000000000000004000000000000000000000000000000000000100000000000000003 x 180 + x 109 + x 34 + 1
361 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000000000000000000000000001 x 181 + x 60 + 1
362 0x4000000000000000000000000000000000000000000100000000000000000000000010000000000000000000003 x 181 + x 94 + x 44 + 1
363 0x8000000000000000000000000000000000000000000000000000000000002000000000000000000000000002081 x 182 + x 61 + x 7 + x 4
364 0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000400000403 x 182 + x 17 + x 5 + 1
365 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd x 183 + x + 1
366 0x40000000000000000000000000000000000000000000000000000000000000000000000000000000000010400003 x 183 + x 14 + x 11 + 1
367 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000200001 x 184 + x 11
368 0x100000000000000000000000000000000000000000000004000000000000000000000000000000000000000000043 x 184 + x 91 + x 3 + 1
369 0x200000000000000000000000000000000000000000000000000000000000000000000080000000000000000000001 x 185 + x 46
370 0x400000000000000000000000000000000000000000000000000000000000010000000000000000000000000010003 x 185 + x 62 + x 8 + 1
371 0x800000000000000000000000000000000000000000000000000000000000022000000000000000080000000000001 x 186 + x 63 + x 61 + x 28
372 0x1000000000000000000000000000000000000000000000000000000000000000000000000000000000100004000003 x 186 + x 22 + x 13 + 1
373 0x2000000000000000000000000000000000000000000000000000000000000080800800000000000000000000000001 x 187 + x 64 + x 60 + x 54
374 0x4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000401003 x 187 + x 11 + x 6 + 1
375 0x8000000000000000000000000000000000000000000000000000000020000000000000000000000000000000000001 x 188 + x 75
376 0x10000000000000000000000000000000000000000000000000000000000000040000000000000000000000000001003 x 188 + x 63 + x 6 + 1
377 0x20000000000000000000000000000000000000000000000000000000000000000000000000000000000020000000001 x 189 + x 21
378 0x40000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000007 x 189 + x 104 + x + 1
379 0x80000000000000000000000000000000000000000000000000000000000000220000000000000000800000000000001 x 190 + x 65 + x 63 + x 30
380 0x100000000000000000000000000000000000000000000000000000000000000000000000000000000000000100040003 x 190 + x 16 + x 9 + 1
381 0x200000000000000000000000000000000000000000000000000000000000000080000000000000000000080000002001 x 191 + x 64 + x 22 + x 7
382 0x400000000000000000000000000000000000000000000000000000000000000000000000000000000004040000000003 x 191 + x 25 + x 21 + 1
383 0x800000000000000000000000000000000000000000000000000000000000008000000000000000000000000000000001 x 192 + x 68
384 0x1000000000000100000000000000000000400000000000000000000000000000000000000000000000000000000000003 x 192 + x 166 + x 125 + 1
385 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000001 x 193 + x 26
386 0x4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010007 x 193 + x 8 + x + 1
387 0x8000000000000000000000000000000000000000000000000000000000000000200000000000000000000000080008001 x 194 + x 65 + x 16 + x 8
388 0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000010001000000003 x 194 + x 26 + x 18 + 1
389 0x20000000000000000000000000000000000000000000000000000000000000008000800000008000000000000000000001 x 195 + x 68 + x 60 + x 44
390 0x40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000014003 x 195 + x 8 + x 7 + 1
391 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000080000001 x 196 + x 16
392 0x100000000000000000000000000000000000000000400000000000000000000000000001000000000000000000000000003 x 196 + x 113 + x 54 + 1
393 0x200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000081 x 197 + x 4
394 0x400000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000007 x 197 + x 60 + x + 1
395 0x800000000000000000000000000000000000000000000000000000000000000002200000000000000000000080000000001 x 198 + x 67 + x 65 + x 22
396 0x1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000043 x 198 + x 12 + x 3 + 1
397 0x3fffff0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 x 199 + x188 + 1
398 0x4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004000013 x 199 + x 13 + x 2 + 1
399 0x8000000000000000000000000000000000000000000000000000000000000000000000002000000000000000000000000001 x 200 + x 55
400 0x10000000000000000000000000000000000000000000000000040000000000000000000000040000000000000000000000003 x 200 + x 99 + x 51 + 1

For many of the polynomials p(x) in the table above, the lowest weight of w(x) is greater than two. As alternative there are some cases where irreducible non-primitive polynomials exist which have w(x) of weight two and lowest degree. Such polynomials are listed here in the range up to m=400.