Information on Result #1750690
Digital (97, 117, 756)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2117, 756, F2, 2, 20) (dual of [(756, 2), 1395, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2117, 1038, F2, 2, 20) (dual of [(1038, 2), 1959, 21]-NRT-code), using
- strength reduction [i] based on linear OOA(2117, 1038, F2, 2, 21) (dual of [(1038, 2), 1959, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2117, 2076, F2, 21) (dual of [2076, 1959, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2117, 2077, F2, 21) (dual of [2077, 1960, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2111, 2049, F2, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(289, 2049, F2, 17) (dual of [2049, 1960, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2117, 2077, F2, 21) (dual of [2077, 1960, 22]-code), using
- OOA 2-folding [i] based on linear OA(2117, 2076, F2, 21) (dual of [2076, 1959, 22]-code), using
- strength reduction [i] based on linear OOA(2117, 1038, F2, 2, 21) (dual of [(1038, 2), 1959, 22]-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.