Information on Result #1315003
Linear OA(2793, 836, F27, 44) (dual of [836, 743, 45]-code), using 93 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 26 times 0, 1, 44 times 0) based on linear OA(2785, 735, F27, 44) (dual of [735, 650, 45]-code), using
- construction XX applied to C1 = C([726,40]), C2 = C([0,41]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([726,41]) [i] based on
- linear OA(2782, 728, F27, 43) (dual of [728, 646, 44]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−2,−1,…,40}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2780, 728, F27, 42) (dual of [728, 648, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2784, 728, F27, 44) (dual of [728, 644, 45]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−2,−1,…,41}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2778, 728, F27, 41) (dual of [728, 650, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [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(2793, 836, F27, 2, 44) (dual of [(836, 2), 1579, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (49, 93, 836)-net over F27 | [i] | ||
| 3 | Linear OOA(2793, 418, F27, 2, 44) (dual of [(418, 2), 743, 45]-NRT-code) | [i] | OOA Folding | |