Information on Result #730832
Linear OA(25635, 775, F256, 21) (dual of [775, 740, 22]-code), using construction XX applied to C1 = C([248,267]), C2 = C([247,266]), C3 = C1 + C2 = C([248,266]), and C∩ = C1 ∩ C2 = C([247,267]) based on
- 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 = {248,249,…,267}, and designed minimum distance d ≥ |I|+1 = 21 [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(25635, 771, F256, 21) (dual of [771, 736, 22]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {247,248,…,267}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(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
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code) (see above)
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(12840, 775, S128, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(25636, 782, F256, 21) (dual of [782, 746, 22]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(25636, 777, F256, 21) (dual of [777, 741, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(25635, 387, F256, 2, 21) (dual of [(387, 2), 739, 22]-NRT-code) | [i] | OOA Folding | |