Information on Result #727203
Linear OA(2792, 738, F27, 47) (dual of [738, 646, 48]-code), using construction XX applied to C1 = C([725,42]), C2 = C([0,43]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([725,43]) based on
- linear OA(2788, 728, F27, 46) (dual of [728, 640, 47]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,42}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2784, 728, F27, 44) (dual of [728, 644, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2790, 728, F27, 47) (dual of [728, 638, 48]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,43}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2782, 728, F27, 43) (dual of [728, 646, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [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(2792, 369, F27, 2, 47) (dual of [(369, 2), 646, 48]-NRT-code) | [i] | OOA Folding | |