Information on Result #730890
Linear OA(25663, 782, F256, 36) (dual of [782, 719, 37]-code), using construction XX applied to C1 = C([112,146]), C2 = C([111,142]), C3 = C1 + C2 = C([112,142]), and C∩ = C1 ∩ C2 = C([111,146]) based on
- linear OA(25658, 771, F256, 35) (dual of [771, 713, 36]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {112,113,…,146}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(25654, 771, F256, 32) (dual of [771, 717, 33]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {111,112,…,142}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(25660, 771, F256, 36) (dual of [771, 711, 37]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {111,112,…,146}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(25652, 771, F256, 31) (dual of [771, 719, 32]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {112,113,…,142}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2563, 9, F256, 3) (dual of [9, 6, 4]-code or 9-arc in PG(2,256) or 9-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), 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: 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 OOA(25663, 391, F256, 2, 36) (dual of [(391, 2), 719, 37]-NRT-code) | [i] | OOA Folding | |