Information on Result #1315014
Linear OA(2795, 843, F27, 45) (dual of [843, 748, 46]-code), using 100 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 28 times 0, 1, 46 times 0) based on linear OA(2787, 735, F27, 45) (dual of [735, 648, 46]-code), using
- construction XX applied to C1 = C([726,41]), C2 = C([0,42]), C3 = C1 + C2 = C([0,41]), and C∩ = C1 ∩ C2 = C([726,42]) [i] based on
- 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(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(2786, 728, F27, 45) (dual of [728, 642, 46]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−2,−1,…,42}, and designed minimum distance d ≥ |I|+1 = 46 [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(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(2795, 843, F27, 2, 45) (dual of [(843, 2), 1591, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (50, 95, 843)-net over F27 | [i] | ||