Information on Result #727121
Linear OA(2780, 732, F27, 42) (dual of [732, 652, 43]-code), using construction XX applied to C1 = C([727,39]), C2 = C([0,40]), C3 = C1 + C2 = C([0,39]), and C∩ = C1 ∩ C2 = C([727,40]) based on
- linear OA(2778, 728, F27, 41) (dual of [728, 650, 42]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,39}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2778, 728, F27, 41) (dual of [728, 650, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2780, 728, F27, 42) (dual of [728, 648, 43]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,40}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2776, 728, F27, 40) (dual of [728, 652, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [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(27105, 796, F27, 42) (dual of [796, 691, 43]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(27106, 800, F27, 42) (dual of [800, 694, 43]-code) | [i] | ||
| 3 | Linear OA(27107, 808, F27, 42) (dual of [808, 701, 43]-code) | [i] | ||
| 4 | Linear OA(27108, 814, F27, 42) (dual of [814, 706, 43]-code) | [i] | ||
| 5 | Linear OA(27109, 816, F27, 42) (dual of [816, 707, 43]-code) | [i] | ||
| 6 | Linear OA(27110, 820, F27, 42) (dual of [820, 710, 43]-code) | [i] | ||
| 7 | Linear OA(2787, 758, F27, 42) (dual of [758, 671, 43]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(2788, 783, F27, 42) (dual of [783, 695, 43]-code) | [i] | ||
| 9 | Linear OA(2789, 825, F27, 42) (dual of [825, 736, 43]-code) | [i] | ||
| 10 | Linear OA(2790, 884, F27, 42) (dual of [884, 794, 43]-code) | [i] | ||
| 11 | Linear OOA(2780, 366, F27, 2, 42) (dual of [(366, 2), 652, 43]-NRT-code) | [i] | OOA Folding | |