Information on Result #1745886
Digital (20, 39, 731)-net over F81, using net defined by OOA based on linear OOA(8139, 731, F81, 21, 19) (dual of [(731, 21), 15312, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8139, 2194, F81, 3, 19) (dual of [(2194, 3), 6543, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8139, 2195, F81, 3, 19) (dual of [(2195, 3), 6546, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8139, 2195, F81, 2, 19) (dual of [(2195, 2), 4351, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8139, 3284, F81, 2, 19) (dual of [(3284, 2), 6529, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8139, 6568, F81, 19) (dual of [6568, 6529, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8139, 6569, F81, 19) (dual of [6569, 6530, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- 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(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-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
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(8139, 6569, F81, 19) (dual of [6569, 6530, 20]-code), using
- OOA 2-folding [i] based on linear OA(8139, 6568, F81, 19) (dual of [6568, 6529, 20]-code), using
- discarding factors / shortening the dual code based on linear OOA(8139, 3284, F81, 2, 19) (dual of [(3284, 2), 6529, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8139, 2195, F81, 2, 19) (dual of [(2195, 2), 4351, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8139, 2195, F81, 3, 19) (dual of [(2195, 3), 6546, 20]-NRT-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.