Information on Result #725825
Linear OA(2756, 758, F27, 24) (dual of [758, 702, 25]-code), using construction XX applied to C1 = C([718,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([718,13]) based on
- linear OA(2745, 728, F27, 23) (dual of [728, 683, 24]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−10,−9,…,12}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2727, 728, F27, 14) (dual of [728, 701, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2747, 728, F27, 24) (dual of [728, 681, 25]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−10,−9,…,13}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2725, 728, F27, 13) (dual of [728, 703, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(279, 28, F27, 9) (dual of [28, 19, 10]-code or 28-arc in PG(8,27)), using
- extended Reed–Solomon code RSe(19,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 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(2756, 379, F27, 2, 24) (dual of [(379, 2), 702, 25]-NRT-code) | [i] | OOA Folding | |