Information on Result #725943
Linear OA(2737, 732, F27, 19) (dual of [732, 695, 20]-code), using construction XX applied to C1 = C([727,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([727,17]) based on
- linear OA(2735, 728, F27, 18) (dual of [728, 693, 19]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2735, 728, F27, 18) (dual of [728, 693, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2737, 728, F27, 19) (dual of [728, 691, 20]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2733, 728, F27, 17) (dual of [728, 695, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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(2746, 760, F27, 19) (dual of [760, 714, 20]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2747, 770, F27, 19) (dual of [770, 723, 20]-code) | [i] | ||
| 3 | Linear OA(2748, 780, F27, 19) (dual of [780, 732, 20]-code) | [i] | ||
| 4 | Linear OA(2749, 784, F27, 19) (dual of [784, 735, 20]-code) | [i] | ||
| 5 | Linear OA(2750, 796, F27, 19) (dual of [796, 746, 20]-code) | [i] | ||
| 6 | Linear OA(2751, 800, F27, 19) (dual of [800, 749, 20]-code) | [i] | ||
| 7 | Linear OA(2752, 838, F27, 19) (dual of [838, 786, 20]-code) | [i] | ||
| 8 | Linear OA(2753, 917, F27, 19) (dual of [917, 864, 20]-code) | [i] | ||
| 9 | Linear OA(2741, 745, F27, 19) (dual of [745, 704, 20]-code) | [i] | Varšamov–Edel Lengthening | |
| 10 | Linear OA(2742, 767, F27, 19) (dual of [767, 725, 20]-code) | [i] | ||
| 11 | Linear OA(2743, 823, F27, 19) (dual of [823, 780, 20]-code) | [i] | ||
| 12 | Linear OA(2744, 937, F27, 19) (dual of [937, 893, 20]-code) | [i] | ||
| 13 | Linear OA(2745, 1111, F27, 19) (dual of [1111, 1066, 20]-code) | [i] | ||
| 14 | Linear OOA(2737, 366, F27, 2, 19) (dual of [(366, 2), 695, 20]-NRT-code) | [i] | OOA Folding | |