Information on Result #730450
Linear OA(12822, 390, F128, 12) (dual of [390, 368, 13]-code), using construction XX applied to C1 = C([378,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([378,8]) based on
- linear OA(12818, 381, F128, 11) (dual of [381, 363, 12]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−3,−2,…,7}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12815, 381, F128, 9) (dual of [381, 366, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(12820, 381, F128, 12) (dual of [381, 361, 13]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−3,−2,…,8}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(12813, 381, F128, 8) (dual of [381, 368, 9]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1282, 7, F128, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 | Linear OA(12871, 16776, F128, 25) (dual of [16776, 16705, 26]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(12869, 16776, F128, 24) (dual of [16776, 16707, 25]-code) | [i] | ||
| 3 | Linear OOA(12822, 195, F128, 2, 12) (dual of [(195, 2), 368, 13]-NRT-code) | [i] | OOA Folding | |