Information on Result #699889
Linear OA(12870, 16426, F128, 29) (dual of [16426, 16356, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,7]) based on
- linear OA(12857, 16385, F128, 29) (dual of [16385, 16328, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(12829, 16385, F128, 15) (dual of [16385, 16356, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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(6482, 16426, S64, 29) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12870, 8213, F128, 2, 29) (dual of [(8213, 2), 16356, 30]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(12870, 5475, F128, 3, 29) (dual of [(5475, 3), 16355, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(12870, 4106, F128, 4, 29) (dual of [(4106, 4), 16354, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(12870, 1173, F128, 29, 29) (dual of [(1173, 29), 33947, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |