Information on Result #725759
Linear OA(2727, 732, F27, 14) (dual of [732, 705, 15]-code), using construction XX applied to C1 = C([727,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([727,12]) based on
- linear OA(2725, 728, F27, 13) (dual of [728, 703, 14]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2725, 728, F27, 13) (dual of [728, 703, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2727, 728, F27, 14) (dual of [728, 701, 15]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2723, 728, F27, 12) (dual of [728, 705, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [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(2734, 760, F27, 14) (dual of [760, 726, 15]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2735, 770, F27, 14) (dual of [770, 735, 15]-code) | [i] | ||
| 3 | Linear OA(2736, 780, F27, 14) (dual of [780, 744, 15]-code) | [i] | ||
| 4 | Linear OA(2737, 788, F27, 14) (dual of [788, 751, 15]-code) | [i] | ||
| 5 | Linear OA(2738, 798, F27, 14) (dual of [798, 760, 15]-code) | [i] | ||
| 6 | Linear OA(2731, 762, F27, 14) (dual of [762, 731, 15]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(2732, 825, F27, 14) (dual of [825, 793, 15]-code) | [i] | ||
| 8 | Linear OA(2733, 971, F27, 14) (dual of [971, 938, 15]-code) | [i] | ||
| 9 | Linear OA(2734, 1219, F27, 14) (dual of [1219, 1185, 15]-code) | [i] | ||
| 10 | Linear OOA(2727, 366, F27, 2, 14) (dual of [(366, 2), 705, 15]-NRT-code) | [i] | OOA Folding | |