Information on Result #727090
Linear OA(2778, 732, F27, 41) (dual of [732, 654, 42]-code), using construction XX applied to C1 = C([727,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([727,39]) based on
- linear OA(2776, 728, F27, 40) (dual of [728, 652, 41]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,38}, and designed minimum distance d ≥ |I|+1 = 41 [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(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(2774, 728, F27, 39) (dual of [728, 654, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [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(27102, 796, F27, 41) (dual of [796, 694, 42]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(27103, 800, F27, 41) (dual of [800, 697, 42]-code) | [i] | ||
| 3 | Linear OA(27104, 808, F27, 41) (dual of [808, 704, 42]-code) | [i] | ||
| 4 | Linear OA(27105, 814, F27, 41) (dual of [814, 709, 42]-code) | [i] | ||
| 5 | Linear OA(27106, 816, F27, 41) (dual of [816, 710, 42]-code) | [i] | ||
| 6 | Linear OA(27107, 820, F27, 41) (dual of [820, 713, 42]-code) | [i] | ||
| 7 | Linear OA(27108, 826, F27, 41) (dual of [826, 718, 42]-code) | [i] | ||
| 8 | Linear OA(27109, 828, F27, 41) (dual of [828, 719, 42]-code) | [i] | ||
| 9 | Linear OA(27110, 830, F27, 41) (dual of [830, 720, 42]-code) | [i] | ||
| 10 | Linear OA(2785, 758, F27, 41) (dual of [758, 673, 42]-code) | [i] | Varšamov–Edel Lengthening | |
| 11 | Linear OA(2786, 781, F27, 41) (dual of [781, 695, 42]-code) | [i] | ||
| 12 | Linear OA(2787, 821, F27, 41) (dual of [821, 734, 42]-code) | [i] | ||
| 13 | Linear OA(2788, 878, F27, 41) (dual of [878, 790, 42]-code) | [i] | ||
| 14 | Linear OA(2789, 949, F27, 41) (dual of [949, 860, 42]-code) | [i] | ||
| 15 | Linear OOA(2778, 366, F27, 2, 41) (dual of [(366, 2), 654, 42]-NRT-code) | [i] | OOA Folding | |