Information on Result #725607
Linear OA(2717, 738, F27, 8) (dual of [738, 721, 9]-code), using construction XX applied to C1 = C([725,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([725,4]) based on
- linear OA(2713, 728, F27, 7) (dual of [728, 715, 8]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,3}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(279, 728, F27, 5) (dual of [728, 719, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2715, 728, F27, 8) (dual of [728, 713, 9]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,4}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(277, 728, F27, 4) (dual of [728, 721, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(272, 8, F27, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- 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(2717, 369, F27, 2, 8) (dual of [(369, 2), 721, 9]-NRT-code) | [i] | OOA Folding | |