Information on Result #730796
Linear OA(25615, 775, F256, 9) (dual of [775, 760, 10]-code), using construction XX applied to C1 = C([254,261]), C2 = C([253,260]), C3 = C1 + C2 = C([254,260]), and C∩ = C1 ∩ C2 = C([253,261]) based on
- linear OA(25613, 771, F256, 8) (dual of [771, 758, 9]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {254,255,…,261}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(25613, 771, F256, 8) (dual of [771, 758, 9]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {253,254,…,260}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(25615, 771, F256, 9) (dual of [771, 756, 10]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {253,254,…,261}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(25611, 771, F256, 7) (dual of [771, 760, 8]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {254,255,…,260}, and designed minimum distance d ≥ |I|+1 = 8 [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 | Linear OA(25652, 66313, F256, 19) (dual of [66313, 66261, 20]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(25650, 66313, F256, 18) (dual of [66313, 66263, 19]-code) | [i] | ||
| 3 | Linear OOA(25615, 775, F256, 2, 9) (dual of [(775, 2), 1535, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(25615, 775, F256, 3, 9) (dual of [(775, 3), 2310, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(25615, 775, F256, 4, 9) (dual of [(775, 4), 3085, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(25615, 775, F256, 5, 9) (dual of [(775, 5), 3860, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(25615, 775, F256, 6, 9) (dual of [(775, 6), 4635, 10]-NRT-code) | [i] | ||
| 8 | Digital (6, 15, 775)-net over F256 | [i] | ||
| 9 | Linear OOA(25615, 387, F256, 2, 9) (dual of [(387, 2), 759, 10]-NRT-code) | [i] | OOA Folding | |