Information on Result #1749341
Digital (55, 67, 686)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(267, 686, F2, 3, 12) (dual of [(686, 3), 1991, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(267, 2058, F2, 12) (dual of [2058, 1991, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(267, 2059, F2, 12) (dual of [2059, 1992, 13]-code), using
- 1 times truncation [i] based on linear OA(268, 2060, F2, 13) (dual of [2060, 1992, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(267, 2048, F2, 13) (dual of [2048, 1981, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(256, 2048, F2, 11) (dual of [2048, 1992, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(268, 2060, F2, 13) (dual of [2060, 1992, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(267, 2059, F2, 12) (dual of [2059, 1992, 13]-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.