Information on Result #1314973
Linear OA(2786, 781, F27, 41) (dual of [781, 695, 42]-code), using 41 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 4 times 0, 1, 11 times 0, 1, 21 times 0) based on 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]) [i] 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: 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 OOA(2786, 762, F27, 2, 41) (dual of [(762, 2), 1438, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (45, 86, 762)-net over F27 | [i] | ||
| 3 | Linear OOA(2786, 390, F27, 2, 41) (dual of [(390, 2), 694, 42]-NRT-code) | [i] | OOA Folding | |