Information on Result #616618

Linear OA(1687, 256, F16, 51) (dual of [256, 169, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(1687, 256, F16, 50) (dual of [256, 169, 51]-code) [i]Strength Reduction
2Linear OA(1687, 256, F16, 49) (dual of [256, 169, 50]-code) [i]
3Linear OA(4174, 512, F4, 51) (dual of [512, 338, 52]-code) [i]Trace Code
4Linear OA(1695, 281, F16, 51) (dual of [281, 186, 52]-code) [i]VarÅ¡amov–Edel Lengthening
5Linear OA(1696, 293, F16, 51) (dual of [293, 197, 52]-code) [i]
6Linear OA(1690, 261, F16, 51) (dual of [261, 171, 52]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
7Linear OA(1691, 260, F16, 53) (dual of [260, 169, 54]-code) [i]✔
8Linear OA(1691, 264, F16, 51) (dual of [264, 173, 52]-code) [i]✔
9Linear OA(1694, 263, F16, 54) (dual of [263, 169, 55]-code) [i]✔
10Linear OA(1692, 267, F16, 51) (dual of [267, 175, 52]-code) [i]✔
11Linear OA(1697, 266, F16, 55) (dual of [266, 169, 56]-code) [i]✔
12Linear OA(1693, 270, F16, 51) (dual of [270, 177, 52]-code) [i]✔
13Linear OA(16100, 269, F16, 56) (dual of [269, 169, 57]-code) [i]✔
14Linear OA(1694, 273, F16, 51) (dual of [273, 179, 52]-code) [i]✔
15Linear OA(16103, 272, F16, 57) (dual of [272, 169, 58]-code) [i]✔
16Linear OA(1696, 277, F16, 51) (dual of [277, 181, 52]-code) [i]✔
17Linear OA(1693, 273, F16, 49) (dual of [273, 180, 50]-code) [i]✔
18Linear OA(1692, 273, F16, 48) (dual of [273, 181, 49]-code) [i]✔
19Linear OA(16107, 276, F16, 58) (dual of [276, 169, 59]-code) [i]✔
20Linear OA(1697, 280, F16, 51) (dual of [280, 183, 52]-code) [i]✔
21Linear OA(16110, 279, F16, 59) (dual of [279, 169, 60]-code) [i]✔
22Linear OA(1699, 284, F16, 51) (dual of [284, 185, 52]-code) [i]✔
23Linear OA(1696, 280, F16, 49) (dual of [280, 184, 50]-code) [i]✔
24Linear OA(1695, 280, F16, 48) (dual of [280, 185, 49]-code) [i]✔
25Linear OA(16114, 283, F16, 60) (dual of [283, 169, 61]-code) [i]✔
26Linear OA(16100, 287, F16, 51) (dual of [287, 187, 52]-code) [i]✔
27Linear OA(16117, 286, F16, 61) (dual of [286, 169, 62]-code) [i]✔
28Linear OA(16101, 289, F16, 51) (dual of [289, 188, 52]-code) [i]✔
29Linear OA(16120, 289, F16, 62) (dual of [289, 169, 63]-code) [i]✔
30Linear OA(16124, 293, F16, 63) (dual of [293, 169, 64]-code) [i]✔
31Linear OA(16130, 299, F16, 66) (dual of [299, 169, 67]-code) [i]✔
32Linear OA(16121, 291, F16, 61) (dual of [291, 170, 62]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
33Linear OA(16114, 284, F16, 59) (dual of [284, 170, 60]-code) [i]✔
34Linear OA(16111, 281, F16, 58) (dual of [281, 170, 59]-code) [i]✔
35Linear OA(16107, 277, F16, 57) (dual of [277, 170, 58]-code) [i]✔
36Linear OA(16104, 274, F16, 56) (dual of [274, 170, 57]-code) [i]✔
37Linear OA(1694, 274, F16, 50) (dual of [274, 180, 51]-code) [i]✔
38Linear OA(1697, 281, F16, 50) (dual of [281, 184, 51]-code) [i]✔
39Linear OOA(1687, 128, F16, 2, 51) (dual of [(128, 2), 169, 52]-NRT-code) [i]OOA Folding