Information on Result #726000
Linear OA(2741, 732, F27, 21) (dual of [732, 691, 22]-code), using construction XX applied to C1 = C([727,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([727,19]) based on
- 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(2739, 728, F27, 20) (dual of [728, 689, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2741, 728, F27, 21) (dual of [728, 687, 22]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,19}, and designed minimum distance d ≥ |I|+1 = 22 [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(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(2752, 770, F27, 21) (dual of [770, 718, 22]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2753, 780, F27, 21) (dual of [780, 727, 22]-code) | [i] | ||
| 3 | Linear OA(2754, 784, F27, 21) (dual of [784, 730, 22]-code) | [i] | ||
| 4 | Linear OA(2755, 796, F27, 21) (dual of [796, 741, 22]-code) | [i] | ||
| 5 | Linear OA(2756, 800, F27, 21) (dual of [800, 744, 22]-code) | [i] | ||
| 6 | Linear OA(2757, 808, F27, 21) (dual of [808, 751, 22]-code) | [i] | ||
| 7 | Linear OA(2758, 839, F27, 21) (dual of [839, 781, 22]-code) | [i] | ||
| 8 | Linear OA(2759, 918, F27, 21) (dual of [918, 859, 22]-code) | [i] | ||
| 9 | Linear OA(2746, 758, F27, 21) (dual of [758, 712, 22]-code) | [i] | Varšamov–Edel Lengthening | |
| 10 | Linear OA(2747, 802, F27, 21) (dual of [802, 755, 22]-code) | [i] | ||
| 11 | Linear OA(2748, 894, F27, 21) (dual of [894, 846, 22]-code) | [i] | ||
| 12 | Linear OA(2749, 1038, F27, 21) (dual of [1038, 989, 22]-code) | [i] | ||
| 13 | Linear OOA(2741, 366, F27, 2, 21) (dual of [(366, 2), 691, 22]-NRT-code) | [i] | OOA Folding | |