Information on Result #725708
Linear OA(2723, 732, F27, 12) (dual of [732, 709, 13]-code), using construction XX applied to C1 = C([727,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([727,10]) based on
- linear OA(2721, 728, F27, 11) (dual of [728, 707, 12]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [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(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(2719, 728, F27, 10) (dual of [728, 709, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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(2796, 20418, F27, 25) (dual of [20418, 20322, 26]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2729, 760, F27, 12) (dual of [760, 731, 13]-code) | [i] | ||
| 3 | Linear OA(2730, 770, F27, 12) (dual of [770, 740, 13]-code) | [i] | ||
| 4 | Linear OA(2731, 780, F27, 12) (dual of [780, 749, 13]-code) | [i] | ||
| 5 | Linear OA(2732, 790, F27, 12) (dual of [790, 758, 13]-code) | [i] | ||
| 6 | Linear OA(2727, 770, F27, 12) (dual of [770, 743, 13]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(2728, 880, F27, 12) (dual of [880, 852, 13]-code) | [i] | ||
| 8 | Linear OA(2729, 1133, F27, 12) (dual of [1133, 1104, 13]-code) | [i] | ||
| 9 | Linear OA(2730, 1519, F27, 12) (dual of [1519, 1489, 13]-code) | [i] | ||
| 10 | Linear OOA(2723, 366, F27, 2, 12) (dual of [(366, 2), 709, 13]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(2723, 122, F27, 12, 12) (dual of [(122, 12), 1441, 13]-NRT-code) | [i] | OA Folding and Stacking | |