Information on Result #1198978
Digital (42, 51, 2105342)-net over F32, using net defined by OOA based on linear OOA(3251, 2105342, F32, 10, 9) (dual of [(2105342, 10), 21053369, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3251, 4210685, F32, 2, 9) (dual of [(4210685, 2), 8421319, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3251, 4210686, F32, 2, 9) (dual of [(4210686, 2), 8421321, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3210, 16385, F32, 2, 4) (dual of [(16385, 2), 32760, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3210, 32770, F32, 4) (dual of [32770, 32760, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, 32771, F32, 4) (dual of [32771, 32761, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(3210, 32768, F32, 4) (dual of [32768, 32758, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(327, 32768, F32, 3) (dual of [32768, 32761, 4]-code or 32768-cap in PG(6,32)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(3210, 32771, F32, 4) (dual of [32771, 32761, 5]-code), using
- OOA 2-folding [i] based on linear OA(3210, 32770, F32, 4) (dual of [32770, 32760, 5]-code), using
- linear OOA(3241, 4194301, F32, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3241, 8388602, F32, 9) (dual of [8388602, 8388561, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- OOA 2-folding [i] based on linear OA(3241, 8388602, F32, 9) (dual of [8388602, 8388561, 10]-code), using
- linear OOA(3210, 16385, F32, 2, 4) (dual of [(16385, 2), 32760, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3251, 4210686, F32, 2, 9) (dual of [(4210686, 2), 8421321, 10]-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.