Information on Result #1199280
Digital (68, 81, 1403903)-net over F32, using net defined by OOA based on linear OOA(3281, 1403903, F32, 14, 13) (dual of [(1403903, 14), 19654561, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3281, 4211710, F32, 2, 13) (dual of [(4211710, 2), 8423339, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3281, 4211711, F32, 2, 13) (dual of [(4211711, 2), 8423341, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3220, 17410, F32, 2, 6) (dual of [(17410, 2), 34800, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(324, 1025, F32, 2, 3) (dual of [(1025, 2), 2046, 4]-NRT-code), using
- linear OOA(3216, 16385, F32, 2, 6) (dual of [(16385, 2), 32754, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3216, 32770, F32, 6) (dual of [32770, 32754, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, 32771, F32, 6) (dual of [32771, 32755, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3216, 32768, F32, 6) (dual of [32768, 32752, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3213, 32768, F32, 5) (dual of [32768, 32755, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(3216, 32771, F32, 6) (dual of [32771, 32755, 7]-code), using
- OOA 2-folding [i] based on linear OA(3216, 32770, F32, 6) (dual of [32770, 32754, 7]-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3261, 4194301, F32, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3261, 8388602, F32, 13) (dual of [8388602, 8388541, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, 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(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- OOA 2-folding [i] based on linear OA(3261, 8388602, F32, 13) (dual of [8388602, 8388541, 14]-code), using
- linear OOA(3220, 17410, F32, 2, 6) (dual of [(17410, 2), 34800, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3281, 4211711, F32, 2, 13) (dual of [(4211711, 2), 8423341, 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.