Information on Result #725723
Linear OA(2725, 732, F27, 13) (dual of [732, 707, 14]-code), using construction XX applied to C1 = C([727,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([727,11]) based on
- linear OA(2723, 728, F27, 12) (dual of [728, 705, 13]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2723, 728, F27, 12) (dual of [728, 705, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2725, 728, F27, 13) (dual of [728, 703, 14]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2721, 728, F27, 11) (dual of [728, 707, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [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(27103, 20414, F27, 27) (dual of [20414, 20311, 28]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2731, 760, F27, 13) (dual of [760, 729, 14]-code) | [i] | ||
| 3 | Linear OA(2732, 770, F27, 13) (dual of [770, 738, 14]-code) | [i] | ||
| 4 | Linear OA(2733, 780, F27, 13) (dual of [780, 747, 14]-code) | [i] | ||
| 5 | Linear OA(2734, 790, F27, 13) (dual of [790, 756, 14]-code) | [i] | ||
| 6 | Linear OA(2735, 839, F27, 13) (dual of [839, 804, 14]-code) | [i] | ||
| 7 | OA(2733, 814, S27, 13) | [i] | ||
| 8 | Linear OA(2729, 766, F27, 13) (dual of [766, 737, 14]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OA(2730, 850, F27, 13) (dual of [850, 820, 14]-code) | [i] | ||
| 10 | Linear OA(2731, 1039, F27, 13) (dual of [1039, 1008, 14]-code) | [i] | ||
| 11 | Linear OA(2732, 1344, F27, 13) (dual of [1344, 1312, 14]-code) | [i] | ||
| 12 | Linear OA(2733, 1763, F27, 13) (dual of [1763, 1730, 14]-code) | [i] | ||
| 13 | Linear OOA(2725, 366, F27, 2, 13) (dual of [(366, 2), 707, 14]-NRT-code) | [i] | OOA Folding | |