Information on Result #1751568
Digital (114, 138, 743)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2138, 743, F2, 2, 24) (dual of [(743, 2), 1348, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2138, 1038, F2, 2, 24) (dual of [(1038, 2), 1938, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2138, 2076, F2, 24) (dual of [2076, 1938, 25]-code), using
- 1 times truncation [i] based on linear OA(2139, 2077, F2, 25) (dual of [2077, 1938, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2133, 2049, F2, 25) (dual of [2049, 1916, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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(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([0,12]) ⊂ C([0,10]) [i] based on
- 1 times truncation [i] based on linear OA(2139, 2077, F2, 25) (dual of [2077, 1938, 26]-code), using
- OOA 2-folding [i] based on linear OA(2138, 2076, F2, 24) (dual of [2076, 1938, 25]-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.