Information on Result #725826
Linear OA(2731, 732, F27, 16) (dual of [732, 701, 17]-code), using construction XX applied to C1 = C([727,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([727,14]) based on
- linear OA(2729, 728, F27, 15) (dual of [728, 699, 16]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2729, 728, F27, 15) (dual of [728, 699, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2731, 728, F27, 16) (dual of [728, 697, 17]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2727, 728, F27, 14) (dual of [728, 701, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [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: Constructive and 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 OA(2739, 760, F27, 16) (dual of [760, 721, 17]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2740, 770, F27, 16) (dual of [770, 730, 17]-code) | [i] | ||
| 3 | Linear OA(2741, 780, F27, 16) (dual of [780, 739, 17]-code) | [i] | ||
| 4 | Linear OA(2742, 784, F27, 16) (dual of [784, 742, 17]-code) | [i] | ||
| 5 | Linear OA(2743, 796, F27, 16) (dual of [796, 753, 17]-code) | [i] | ||
| 6 | Linear OA(2744, 800, F27, 16) (dual of [800, 756, 17]-code) | [i] | ||
| 7 | Linear OA(2735, 753, F27, 16) (dual of [753, 718, 17]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(2736, 791, F27, 16) (dual of [791, 755, 17]-code) | [i] | ||
| 9 | Linear OA(2737, 885, F27, 16) (dual of [885, 848, 17]-code) | [i] | ||
| 10 | Linear OA(2738, 1060, F27, 16) (dual of [1060, 1022, 17]-code) | [i] | ||
| 11 | Linear OA(2739, 1310, F27, 16) (dual of [1310, 1271, 17]-code) | [i] | ||
| 12 | Linear OA(2740, 1629, F27, 16) (dual of [1629, 1589, 17]-code) | [i] | ||
| 13 | Linear OOA(2731, 366, F27, 2, 16) (dual of [(366, 2), 701, 17]-NRT-code) | [i] | OOA Folding | |