Information on Result #1747818
Digital (29, 56, 1328)-net over F128, using net defined by OOA based on linear OOA(12856, 1328, F128, 36, 27) (dual of [(1328, 36), 47752, 28]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(12856, 5313, F128, 4, 27) (dual of [(5313, 4), 21196, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12856, 5315, F128, 4, 27) (dual of [(5315, 4), 21204, 28]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12856, 5315, F128, 3, 27) (dual of [(5315, 3), 15889, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12856, 5465, F128, 3, 27) (dual of [(5465, 3), 16339, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12856, 16395, F128, 27) (dual of [16395, 16339, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(12856, 16396, F128, 27) (dual of [16396, 16340, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [i] based on
- linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(12845, 16385, F128, 23) (dual of [16385, 16340, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12856, 16396, F128, 27) (dual of [16396, 16340, 28]-code), using
- OOA 3-folding [i] based on linear OA(12856, 16395, F128, 27) (dual of [16395, 16339, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(12856, 5465, F128, 3, 27) (dual of [(5465, 3), 16339, 28]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12856, 5315, F128, 3, 27) (dual of [(5315, 3), 15889, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12856, 5315, F128, 4, 27) (dual of [(5315, 4), 21204, 28]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.