Information on Result #730873
Linear OA(25650, 775, F256, 30) (dual of [775, 725, 31]-code), using construction XX applied to C1 = C([115,143]), C2 = C([114,142]), C3 = C1 + C2 = C([115,142]), and C∩ = C1 ∩ C2 = C([114,143]) based on
- linear OA(25648, 771, F256, 29) (dual of [771, 723, 30]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {115,116,…,143}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(25648, 771, F256, 29) (dual of [771, 723, 30]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {114,115,…,142}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(25650, 771, F256, 30) (dual of [771, 721, 31]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {114,115,…,143}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(25646, 771, F256, 28) (dual of [771, 725, 29]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {115,116,…,142}, and designed minimum distance d ≥ |I|+1 = 29 [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(12858, 775, S128, 30) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(25651, 810, F256, 30) (dual of [810, 759, 31]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OOA(25650, 387, F256, 2, 30) (dual of [(387, 2), 724, 31]-NRT-code) | [i] | OOA Folding | |