Information on Result #1227716
Digital (54, 68, 1200560)-net over F81, using (u, u+v)-construction based on
- digital (8, 15, 2189)-net over F81, using
- net defined by OOA [i] based on linear OOA(8115, 2189, F81, 7, 7) (dual of [(2189, 7), 15308, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(8115, 6568, F81, 7) (dual of [6568, 6553, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(8115, 6569, F81, 7) (dual of [6569, 6554, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(8113, 6561, F81, 7) (dual of [6561, 6548, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(817, 6561, F81, 4) (dual of [6561, 6554, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(6) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(8115, 6569, F81, 7) (dual of [6569, 6554, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(8115, 6568, F81, 7) (dual of [6568, 6553, 8]-code), using
- net defined by OOA [i] based on linear OOA(8115, 2189, F81, 7, 7) (dual of [(2189, 7), 15308, 8]-NRT-code), using
- digital (39, 53, 1198371)-net over F81, using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-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.