Information on Result #725612
Linear OA(2713, 732, F27, 7) (dual of [732, 719, 8]-code), using construction XX applied to C1 = C([727,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([727,5]) based on
- linear OA(2711, 728, F27, 6) (dual of [728, 717, 7]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2711, 728, F27, 6) (dual of [728, 717, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2713, 728, F27, 7) (dual of [728, 715, 8]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(279, 728, F27, 5) (dual of [728, 719, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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(2756, 20418, F27, 15) (dual of [20418, 20362, 16]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2770, 532177, F27, 15) (dual of [532177, 532107, 16]-code) | [i] | ||
| 3 | Linear OA(2716, 760, F27, 7) (dual of [760, 744, 8]-code) | [i] | ||
| 4 | Linear OA(2717, 1462, F27, 7) (dual of [1462, 1445, 8]-code) | [i] | ||
| 5 | Linear OA(2715, 753, F27, 7) (dual of [753, 738, 8]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(2716, 893, F27, 7) (dual of [893, 877, 8]-code) | [i] | ||
| 7 | Linear OA(2718, 2274, F27, 7) (dual of [2274, 2256, 8]-code) | [i] | ||
| 8 | Linear OOA(2713, 366, F27, 2, 7) (dual of [(366, 2), 719, 8]-NRT-code) | [i] | OOA Folding | |