Information on Result #699888
Linear OA(12874, 16426, F128, 31) (dual of [16426, 16352, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,8]) based on
- linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(12813, 41, F128, 13) (dual of [41, 28, 14]-code or 41-arc in PG(12,128)), using
- discarding factors / shortening the dual code based on linear OA(12813, 128, F128, 13) (dual of [128, 115, 14]-code or 128-arc in PG(12,128)), using
- Reed–Solomon code RS(115,128) [i]
- discarding factors / shortening the dual code based on linear OA(12813, 128, F128, 13) (dual of [128, 115, 14]-code or 128-arc in PG(12,128)), using
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | OA(6487, 16426, S64, 31) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12874, 16426, F128, 2, 31) (dual of [(16426, 2), 32778, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12874, 16426, F128, 3, 31) (dual of [(16426, 3), 49204, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(12874, 16426, F128, 4, 31) (dual of [(16426, 4), 65630, 32]-NRT-code) | [i] | ||
| 5 | Digital (43, 74, 16426)-net over F128 | [i] | ||
| 6 | Linear OOA(12874, 8213, F128, 2, 31) (dual of [(8213, 2), 16352, 32]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12874, 5475, F128, 3, 31) (dual of [(5475, 3), 16351, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(12874, 4106, F128, 4, 31) (dual of [(4106, 4), 16350, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(12874, 1095, F128, 31, 31) (dual of [(1095, 31), 33871, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |