Information on Result #730861
Linear OA(25645, 775, F256, 27) (dual of [775, 730, 28]-code), using construction XX applied to C1 = C([245,270]), C2 = C([244,269]), C3 = C1 + C2 = C([245,269]), and C∩ = C1 ∩ C2 = C([244,270]) based on
- linear OA(25643, 771, F256, 26) (dual of [771, 728, 27]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {245,246,…,270}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(25643, 771, F256, 26) (dual of [771, 728, 27]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {244,245,…,269}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(25645, 771, F256, 27) (dual of [771, 726, 28]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {244,245,…,270}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25641, 771, F256, 25) (dual of [771, 730, 26]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {245,246,…,269}, and designed minimum distance d ≥ |I|+1 = 26 [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(12852, 775, S128, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(25646, 792, F256, 27) (dual of [792, 746, 28]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(25646, 777, F256, 27) (dual of [777, 731, 28]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(25645, 387, F256, 2, 27) (dual of [(387, 2), 729, 28]-NRT-code) | [i] | OOA Folding | |