Information on Result #1314709
Linear OA(278, 786, F27, 4) (dual of [786, 778, 5]-code), using 53 step Varšamov–Edel lengthening with (ri) = (1, 52 times 0) based on linear OA(277, 732, F27, 4) (dual of [732, 725, 5]-code), using
- construction XX applied to C1 = C([727,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([727,2]) [i] based on
- linear OA(275, 728, F27, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [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(277, 728, F27, 4) (dual of [728, 721, 5]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [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
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
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(278, 786, F27, 2, 4) (dual of [(786, 2), 1564, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (4, 8, 786)-net over F27 | [i] | ||