Information on Result #726172
Linear OA(2765, 750, F27, 31) (dual of [750, 685, 32]-code), using construction XX applied to C1 = C([727,28]), C2 = C([7,29]), C3 = C1 + C2 = C([7,28]), and C∩ = C1 ∩ C2 = C([727,29]) based on
- linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,28}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2745, 728, F27, 23) (dual of [728, 683, 24]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {7,8,…,29}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2758, 728, F27, 31) (dual of [728, 670, 32]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,29}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2743, 728, F27, 22) (dual of [728, 685, 23]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {7,8,…,28}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(277, 20, F27, 7) (dual of [20, 13, 8]-code or 20-arc in PG(6,27)), using
- discarding factors / shortening the dual code based on linear OA(277, 27, F27, 7) (dual of [27, 20, 8]-code or 27-arc in PG(6,27)), using
- Reed–Solomon code RS(20,27) [i]
- discarding factors / shortening the dual code based on linear OA(277, 27, F27, 7) (dual of [27, 20, 8]-code or 27-arc in PG(6,27)), using
- 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
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 OOA(2765, 375, F27, 2, 31) (dual of [(375, 2), 685, 32]-NRT-code) | [i] | OOA Folding | |