Information on Result #727028
Linear OA(2774, 732, F27, 39) (dual of [732, 658, 40]-code), using construction XX applied to C1 = C([727,36]), C2 = C([0,37]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([727,37]) based on
- linear OA(2772, 728, F27, 38) (dual of [728, 656, 39]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,36}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2772, 728, F27, 38) (dual of [728, 656, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2774, 728, F27, 39) (dual of [728, 654, 40]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,37}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2770, 728, F27, 37) (dual of [728, 658, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [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(2797, 796, F27, 39) (dual of [796, 699, 40]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2798, 800, F27, 39) (dual of [800, 702, 40]-code) | [i] | ||
| 3 | Linear OA(2799, 808, F27, 39) (dual of [808, 709, 40]-code) | [i] | ||
| 4 | Linear OA(27100, 814, F27, 39) (dual of [814, 714, 40]-code) | [i] | ||
| 5 | Linear OA(27101, 816, F27, 39) (dual of [816, 715, 40]-code) | [i] | ||
| 6 | Linear OA(27102, 820, F27, 39) (dual of [820, 718, 40]-code) | [i] | ||
| 7 | Linear OA(27103, 826, F27, 39) (dual of [826, 723, 40]-code) | [i] | ||
| 8 | Linear OA(27104, 828, F27, 39) (dual of [828, 724, 40]-code) | [i] | ||
| 9 | Linear OA(27105, 830, F27, 39) (dual of [830, 725, 40]-code) | [i] | ||
| 10 | Linear OA(27106, 832, F27, 39) (dual of [832, 726, 40]-code) | [i] | ||
| 11 | Linear OA(27107, 840, F27, 39) (dual of [840, 733, 40]-code) | [i] | ||
| 12 | Linear OA(27108, 844, F27, 39) (dual of [844, 736, 40]-code) | [i] | ||
| 13 | Linear OA(27109, 918, F27, 39) (dual of [918, 809, 40]-code) | [i] | ||
| 14 | Linear OA(27110, 1100, F27, 39) (dual of [1100, 990, 40]-code) | [i] | ||
| 15 | Linear OA(2781, 756, F27, 39) (dual of [756, 675, 40]-code) | [i] | Varšamov–Edel Lengthening | |
| 16 | Linear OA(2782, 777, F27, 39) (dual of [777, 695, 40]-code) | [i] | ||
| 17 | Linear OA(2783, 813, F27, 39) (dual of [813, 730, 40]-code) | [i] | ||
| 18 | Linear OA(2784, 868, F27, 39) (dual of [868, 784, 40]-code) | [i] | ||
| 19 | Linear OA(2785, 940, F27, 39) (dual of [940, 855, 40]-code) | [i] | ||
| 20 | Linear OOA(2774, 366, F27, 2, 39) (dual of [(366, 2), 658, 40]-NRT-code) | [i] | OOA Folding | |