Information on Result #1202402
Digital (48, 61, 1399194)-net over F81, using net defined by OOA based on linear OOA(8161, 1399194, F81, 14, 13) (dual of [(1399194, 14), 19588655, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8161, 4197583, F81, 2, 13) (dual of [(4197583, 2), 8395105, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8161, 4197584, F81, 2, 13) (dual of [(4197584, 2), 8395107, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8112, 3283, F81, 2, 6) (dual of [(3283, 2), 6554, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8112, 6566, F81, 6) (dual of [6566, 6554, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- OOA 2-folding [i] based on linear OA(8112, 6566, F81, 6) (dual of [6566, 6554, 7]-code), using
- linear OOA(8149, 4194301, F81, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8149, 8388602, F81, 13) (dual of [8388602, 8388553, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- OOA 2-folding [i] based on linear OA(8149, 8388602, F81, 13) (dual of [8388602, 8388553, 14]-code), using
- linear OOA(8112, 3283, F81, 2, 6) (dual of [(3283, 2), 6554, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8161, 4197584, F81, 2, 13) (dual of [(4197584, 2), 8395107, 14]-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.