Information on Result #1314712
Linear OA(2715, 1978, F27, 6) (dual of [1978, 1963, 7]-code), using 1240 step Varšamov–Edel lengthening with (ri) = (1, 24 times 0, 1, 296 times 0, 1, 917 times 0) based on linear OA(2712, 735, F27, 6) (dual of [735, 723, 7]-code), using
- construction XX applied to C1 = C([726,2]), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C([726,3]) [i] based on
- linear OA(279, 728, F27, 5) (dual of [728, 719, 6]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−2,−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 6 [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(2711, 728, F27, 6) (dual of [728, 717, 7]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−2,−1,…,3}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(275, 728, F27, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(271, 5, F27, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- Reed–Solomon code RS(26,27) [i]
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), 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: 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(2715, 1978, F27, 2, 6) (dual of [(1978, 2), 3941, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (9, 15, 1978)-net over F27 | [i] | ||
| 3 | Linear OOA(2715, 989, F27, 2, 6) (dual of [(989, 2), 1963, 7]-NRT-code) | [i] | OOA Folding | |