Information on Result #1202790
Digital (31, 51, 679)-net over F81, using net defined by OOA based on linear OOA(8151, 679, F81, 22, 20) (dual of [(679, 22), 14887, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8151, 3396, F81, 2, 20) (dual of [(3396, 2), 6741, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8151, 3397, F81, 2, 20) (dual of [(3397, 2), 6743, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8112, 116, F81, 2, 10) (dual of [(116, 2), 220, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,221P) [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- linear OOA(8139, 3281, F81, 2, 20) (dual of [(3281, 2), 6523, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8139, 6562, F81, 20) (dual of [6562, 6523, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8139, 6563, F81, 20) (dual of [6563, 6524, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(8139, 6563, F81, 20) (dual of [6563, 6524, 21]-code), using
- OOA 2-folding [i] based on linear OA(8139, 6562, F81, 20) (dual of [6562, 6523, 21]-code), using
- linear OOA(8112, 116, F81, 2, 10) (dual of [(116, 2), 220, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8151, 3397, F81, 2, 20) (dual of [(3397, 2), 6743, 21]-NRT-code), using
Mode: Constructive and 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.