Information on Result #1751287
Digital (109, 132, 723)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2132, 723, F2, 2, 23) (dual of [(723, 2), 1314, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2132, 1040, F2, 2, 23) (dual of [(1040, 2), 1948, 24]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2128, 1038, F2, 2, 23) (dual of [(1038, 2), 1948, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2128, 2076, F2, 23) (dual of [2076, 1948, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2100, 2048, F2, 19) (dual of [2048, 1948, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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 Ce(22) ⊂ Ce(18) [i] based on
- OOA 2-folding [i] based on linear OA(2128, 2076, F2, 23) (dual of [2076, 1948, 24]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2128, 1038, F2, 2, 23) (dual of [(1038, 2), 1948, 24]-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.