Information on Result #1749594
Digital (68, 80, 2735)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(280, 2735, F2, 3, 12) (dual of [(2735, 3), 8125, 13]-NRT-code), using
- strength reduction [i] based on linear OOA(280, 2735, F2, 3, 13) (dual of [(2735, 3), 8125, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(280, 8205, F2, 13) (dual of [8205, 8125, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(280, 8206, F2, 13) (dual of [8206, 8126, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(279, 8192, F2, 13) (dual of [8192, 8113, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(266, 8192, F2, 11) (dual of [8192, 8126, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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
- discarding factors / shortening the dual code based on linear OA(280, 8206, F2, 13) (dual of [8206, 8126, 14]-code), using
- OOA 3-folding [i] based on linear OA(280, 8205, F2, 13) (dual of [8205, 8125, 14]-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.