Information on Result #1316284
Linear OA(25635, 864, F256, 20) (dual of [864, 829, 21]-code), using 87 step Varšamov–Edel lengthening with (ri) = (1, 86 times 0) based on linear OA(25634, 776, F256, 20) (dual of [776, 742, 21]-code), using
- construction XX applied to C1 = C([248,266]), C2 = C([247,264]), C3 = C1 + C2 = C([248,264]), and C∩ = C1 ∩ C2 = C([247,266]) [i] based on
- linear OA(25631, 771, F256, 19) (dual of [771, 740, 20]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {248,249,…,266}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25631, 771, F256, 18) (dual of [771, 740, 19]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {247,248,…,264}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(25633, 771, F256, 20) (dual of [771, 738, 21]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {247,248,…,266}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(25629, 771, F256, 17) (dual of [771, 742, 18]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {248,249,…,264}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, 256, F256, 1) (dual of [256, 255, 2]-code), using
- Reed–Solomon code RS(255,256) [i]
- discarding factors / shortening the dual code based on linear OA(2561, 256, F256, 1) (dual of [256, 255, 2]-code), using
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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(25635, 864, F256, 2, 20) (dual of [(864, 2), 1693, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25635, 864, F256, 3, 20) (dual of [(864, 3), 2557, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(25635, 864, F256, 4, 20) (dual of [(864, 4), 3421, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(25635, 864, F256, 5, 20) (dual of [(864, 5), 4285, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(25635, 864, F256, 6, 20) (dual of [(864, 6), 5149, 21]-NRT-code) | [i] | ||
| 6 | Digital (15, 35, 864)-net over F256 | [i] | ||