Information on Result #726907
Linear OA(2780, 744, F27, 40) (dual of [744, 664, 41]-code), using construction XX applied to C1 = C([723,33]), C2 = C([0,34]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([723,34]) based on
- linear OA(2774, 728, F27, 39) (dual of [728, 654, 40]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−5,−4,…,33}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2766, 728, F27, 35) (dual of [728, 662, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2776, 728, F27, 40) (dual of [728, 652, 41]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−5,−4,…,34}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2764, 728, F27, 34) (dual of [728, 664, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(274, 14, F27, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,27)), using
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- Reed–Solomon code RS(23,27) [i]
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), 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 OA(27110, 838, F27, 40) (dual of [838, 728, 41]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(2780, 372, F27, 2, 40) (dual of [(372, 2), 664, 41]-NRT-code) | [i] | OOA Folding | |