Information on Result #1316294
Linear OA(25640, 864, F256, 23) (dual of [864, 824, 24]-code), using 87 step Varšamov–Edel lengthening with (ri) = (1, 86 times 0) based on linear OA(25639, 776, F256, 23) (dual of [776, 737, 24]-code), using
- construction XX applied to C1 = C([118,139]), C2 = C([117,137]), C3 = C1 + C2 = C([118,137]), and C∩ = C1 ∩ C2 = C([117,139]) [i] based on
- linear OA(25636, 771, F256, 22) (dual of [771, 735, 23]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {118,119,…,139}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25636, 771, F256, 21) (dual of [771, 735, 22]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {117,118,…,137}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25638, 771, F256, 23) (dual of [771, 733, 24]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {117,118,…,139}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25634, 771, F256, 20) (dual of [771, 737, 21]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {118,119,…,137}, and designed minimum distance d ≥ |I|+1 = 21 [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(25640, 864, F256, 2, 23) (dual of [(864, 2), 1688, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25640, 864, F256, 3, 23) (dual of [(864, 3), 2552, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(25640, 864, F256, 4, 23) (dual of [(864, 4), 3416, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(25640, 864, F256, 5, 23) (dual of [(864, 5), 4280, 24]-NRT-code) | [i] | ||
| 5 | Linear OOA(25640, 864, F256, 6, 23) (dual of [(864, 6), 5144, 24]-NRT-code) | [i] | ||
| 6 | Digital (17, 40, 864)-net over F256 | [i] | ||