Information on Result #1812411
Digital (20, 38, 3049)-net over F81, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(8138, 3049, F81, 2, 18) (dual of [(3049, 2), 6060, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8138, 3286, F81, 2, 18) (dual of [(3286, 2), 6534, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8138, 6572, F81, 18) (dual of [6572, 6534, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- OOA 2-folding [i] based on linear OA(8138, 6572, F81, 18) (dual of [6572, 6534, 19]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.