Information on Result #726270
Linear OA(2751, 732, F27, 26) (dual of [732, 681, 27]-code), using construction XX applied to C1 = C([727,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([727,24]) based on
- linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2751, 728, F27, 26) (dual of [728, 677, 27]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,24}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2747, 728, F27, 24) (dual of [728, 681, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [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(2766, 780, F27, 26) (dual of [780, 714, 27]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2767, 784, F27, 26) (dual of [784, 717, 27]-code) | [i] | ||
| 3 | Linear OA(2768, 796, F27, 26) (dual of [796, 728, 27]-code) | [i] | ||
| 4 | Linear OA(2769, 800, F27, 26) (dual of [800, 731, 27]-code) | [i] | ||
| 5 | Linear OA(2770, 808, F27, 26) (dual of [808, 738, 27]-code) | [i] | ||
| 6 | Linear OA(2771, 814, F27, 26) (dual of [814, 743, 27]-code) | [i] | ||
| 7 | Linear OA(2772, 816, F27, 26) (dual of [816, 744, 27]-code) | [i] | ||
| 8 | Linear OA(2773, 838, F27, 26) (dual of [838, 765, 27]-code) | [i] | ||
| 9 | Linear OA(2774, 841, F27, 26) (dual of [841, 767, 27]-code) | [i] | ||
| 10 | Linear OA(2756, 750, F27, 26) (dual of [750, 694, 27]-code) | [i] | Varšamov–Edel Lengthening | |
| 11 | Linear OA(2757, 780, F27, 26) (dual of [780, 723, 27]-code) | [i] | ||
| 12 | Linear OA(2758, 845, F27, 26) (dual of [845, 787, 27]-code) | [i] | ||
| 13 | Linear OA(2759, 949, F27, 26) (dual of [949, 890, 27]-code) | [i] | ||
| 14 | Linear OOA(2751, 366, F27, 2, 26) (dual of [(366, 2), 681, 27]-NRT-code) | [i] | OOA Folding | |