Information on Result #1814283
Digital (39, 78, 4095)-net over F128, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12878, 4095, F128, 4, 39) (dual of [(4095, 4), 16302, 40]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12878, 4097, F128, 4, 39) (dual of [(4097, 4), 16310, 40]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12878, 16388, F128, 39) (dual of [16388, 16310, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(12878, 16390, F128, 39) (dual of [16390, 16312, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(12877, 16385, F128, 39) (dual of [16385, 16308, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(12873, 16385, F128, 37) (dual of [16385, 16312, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12878, 16390, F128, 39) (dual of [16390, 16312, 40]-code), using
- OOA 4-folding [i] based on linear OA(12878, 16388, F128, 39) (dual of [16388, 16310, 40]-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.