Information on Result #1303809
Linear OA(16117, 131096, F16, 28) (dual of [131096, 130979, 29]-code), using construction X with Varšamov bound based on
- linear OA(16116, 131094, F16, 28) (dual of [131094, 130978, 29]-code), using
- trace code [i] based on linear OA(25658, 65547, F256, 28) (dual of [65547, 65489, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- trace code [i] based on linear OA(25658, 65547, F256, 28) (dual of [65547, 65489, 29]-code), using
- linear OA(16116, 131095, F16, 27) (dual of [131095, 130979, 28]-code), using Gilbert–Varšamov bound and bm = 16116 > Vbs−1(k−1) = 106865 100410 059336 493689 566262 774517 037532 435818 553780 201088 950113 998220 340500 699264 034343 206138 276068 484675 062726 708095 154619 255704 027136 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(16117, 131096, F16, 2, 28) (dual of [(131096, 2), 262075, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (89, 117, 131096)-net over F16 | [i] | ||
| 3 | Linear OOA(16117, 65548, F16, 2, 28) (dual of [(65548, 2), 130979, 29]-NRT-code) | [i] | OOA Folding | |