Information on Result #1314731
Linear OA(2726, 2182, F27, 10) (dual of [2182, 2156, 11]-code), using 1443 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 16 times 0, 1, 77 times 0, 1, 236 times 0, 1, 442 times 0, 1, 664 times 0) based on linear OA(2719, 732, F27, 10) (dual of [732, 713, 11]-code), using
- construction XX applied to C1 = C([727,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([727,8]) [i] based on
- linear OA(2717, 728, F27, 9) (dual of [728, 711, 10]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2717, 728, F27, 9) (dual of [728, 711, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2719, 728, F27, 10) (dual of [728, 709, 11]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2715, 728, F27, 8) (dual of [728, 713, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [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(2726, 2182, F27, 2, 10) (dual of [(2182, 2), 4338, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (16, 26, 2182)-net over F27 | [i] | ||
| 3 | Linear OOA(2726, 1091, F27, 2, 10) (dual of [(1091, 2), 2156, 11]-NRT-code) | [i] | OOA Folding | |