Information on Result #726611
Linear OA(2758, 732, F27, 31) (dual of [732, 674, 32]-code), using construction XX applied to C1 = C([727,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([727,29]) based on
- linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,28}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2758, 728, F27, 31) (dual of [728, 670, 32]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,29}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2754, 728, F27, 29) (dual of [728, 674, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [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(2775, 780, F27, 31) (dual of [780, 705, 32]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2776, 784, F27, 31) (dual of [784, 708, 32]-code) | [i] | ||
| 3 | Linear OA(2777, 796, F27, 31) (dual of [796, 719, 32]-code) | [i] | ||
| 4 | Linear OA(2778, 800, F27, 31) (dual of [800, 722, 32]-code) | [i] | ||
| 5 | Linear OA(2779, 808, F27, 31) (dual of [808, 729, 32]-code) | [i] | ||
| 6 | Linear OA(2780, 814, F27, 31) (dual of [814, 734, 32]-code) | [i] | ||
| 7 | Linear OA(2781, 816, F27, 31) (dual of [816, 735, 32]-code) | [i] | ||
| 8 | Linear OA(2782, 820, F27, 31) (dual of [820, 738, 32]-code) | [i] | ||
| 9 | Linear OA(2783, 826, F27, 31) (dual of [826, 743, 32]-code) | [i] | ||
| 10 | Linear OA(2784, 840, F27, 31) (dual of [840, 756, 32]-code) | [i] | ||
| 11 | Linear OA(2785, 916, F27, 31) (dual of [916, 831, 32]-code) | [i] | ||
| 12 | Linear OA(2786, 1098, F27, 31) (dual of [1098, 1012, 32]-code) | [i] | ||
| 13 | OA(2778, 814, S27, 31) | [i] | ||
| 14 | Linear OA(2765, 753, F27, 31) (dual of [753, 688, 32]-code) | [i] | Varšamov–Edel Lengthening | |
| 15 | Linear OA(2766, 770, F27, 31) (dual of [770, 704, 32]-code) | [i] | ||
| 16 | Linear OA(2767, 800, F27, 31) (dual of [800, 733, 32]-code) | [i] | ||
| 17 | Linear OA(2768, 852, F27, 31) (dual of [852, 784, 32]-code) | [i] | ||
| 18 | Linear OA(2769, 929, F27, 31) (dual of [929, 860, 32]-code) | [i] | ||
| 19 | Linear OA(2770, 1029, F27, 31) (dual of [1029, 959, 32]-code) | [i] | ||
| 20 | Linear OOA(2758, 366, F27, 2, 31) (dual of [(366, 2), 674, 32]-NRT-code) | [i] | OOA Folding | |