Information on Result #725977
Linear OA(2739, 732, F27, 20) (dual of [732, 693, 21]-code), using construction XX applied to C1 = C([727,17]), C2 = C([0,18]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([727,18]) based on
- 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(2737, 728, F27, 19) (dual of [728, 691, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2739, 728, F27, 20) (dual of [728, 689, 21]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [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(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(2750, 770, F27, 20) (dual of [770, 720, 21]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2751, 780, F27, 20) (dual of [780, 729, 21]-code) | [i] | ||
| 3 | Linear OA(2752, 784, F27, 20) (dual of [784, 732, 21]-code) | [i] | ||
| 4 | Linear OA(2753, 796, F27, 20) (dual of [796, 743, 21]-code) | [i] | ||
| 5 | Linear OA(2754, 800, F27, 20) (dual of [800, 746, 21]-code) | [i] | ||
| 6 | Linear OA(2755, 808, F27, 20) (dual of [808, 753, 21]-code) | [i] | ||
| 7 | Linear OA(2756, 839, F27, 20) (dual of [839, 783, 21]-code) | [i] | ||
| 8 | Linear OA(2744, 762, F27, 20) (dual of [762, 718, 21]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OA(2745, 811, F27, 20) (dual of [811, 766, 21]-code) | [i] | ||
| 10 | Linear OA(2746, 913, F27, 20) (dual of [913, 867, 21]-code) | [i] | ||
| 11 | Linear OA(2747, 1071, F27, 20) (dual of [1071, 1024, 21]-code) | [i] | ||
| 12 | Linear OA(2748, 1270, F27, 20) (dual of [1270, 1222, 21]-code) | [i] | ||
| 13 | Linear OOA(2739, 366, F27, 2, 20) (dual of [(366, 2), 693, 21]-NRT-code) | [i] | OOA Folding | |