Information on Result #1316163
Linear OA(12826, 411, F128, 15) (dual of [411, 385, 16]-code), using 25 step Varšamov–Edel lengthening with (ri) = (1, 24 times 0) based on linear OA(12825, 385, F128, 15) (dual of [385, 360, 16]-code), using
- construction XX applied to C1 = C([380,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([380,13]) [i] based on
- linear OA(12823, 381, F128, 14) (dual of [381, 358, 15]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(12823, 381, F128, 14) (dual of [381, 358, 15]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(12825, 381, F128, 15) (dual of [381, 356, 16]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12821, 381, F128, 13) (dual of [381, 360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code) (see above)
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(12826, 411, F128, 2, 15) (dual of [(411, 2), 796, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12826, 411, F128, 3, 15) (dual of [(411, 3), 1207, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(12826, 411, F128, 4, 15) (dual of [(411, 4), 1618, 16]-NRT-code) | [i] | ||
| 4 | Digital (11, 26, 411)-net over F128 | [i] | ||