Information on Result #727288
Linear OA(2798, 732, F27, 51) (dual of [732, 634, 52]-code), using construction XX applied to C1 = C([727,48]), C2 = C([0,49]), C3 = C1 + C2 = C([0,48]), and C∩ = C1 ∩ C2 = C([727,49]) based on
- linear OA(2796, 728, F27, 50) (dual of [728, 632, 51]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,48}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2796, 728, F27, 50) (dual of [728, 632, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2798, 728, F27, 51) (dual of [728, 630, 52]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,49}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2794, 728, F27, 49) (dual of [728, 634, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [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(27104, 763, F27, 51) (dual of [763, 659, 52]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(27105, 793, F27, 51) (dual of [793, 688, 52]-code) | [i] | ||
| 3 | Linear OA(27106, 838, F27, 51) (dual of [838, 732, 52]-code) | [i] | ||
| 4 | Linear OOA(2798, 366, F27, 2, 51) (dual of [(366, 2), 634, 52]-NRT-code) | [i] | OOA Folding | |