Information on Result #730314
Linear OA(8177, 418, F81, 42) (dual of [418, 341, 43]-code), using construction XX applied to C1 = C([21,61]), C2 = C([20,58]), C3 = C1 + C2 = C([21,58]), and C∩ = C1 ∩ C2 = C([20,61]) based on
- linear OA(8173, 410, F81, 41) (dual of [410, 337, 42]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {21,22,…,61}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(8171, 410, F81, 39) (dual of [410, 339, 40]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {20,21,…,58}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(8175, 410, F81, 42) (dual of [410, 335, 43]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {20,21,…,61}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(8169, 410, F81, 38) (dual of [410, 341, 39]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {21,22,…,58}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(812, 6, F81, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 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(8177, 209, F81, 2, 42) (dual of [(209, 2), 341, 43]-NRT-code) | [i] | OOA Folding | |