Information on Result #1813162
Digital (39, 78, 2120)-net over F81, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(8178, 2120, F81, 3, 39) (dual of [(2120, 3), 6282, 40]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8178, 2189, F81, 3, 39) (dual of [(2189, 3), 6489, 40]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8178, 6567, F81, 39) (dual of [6567, 6489, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(8177, 6562, F81, 39) (dual of [6562, 6485, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(8173, 6562, F81, 37) (dual of [6562, 6489, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 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
- OOA 3-folding [i] based on linear OA(8178, 6567, F81, 39) (dual of [6567, 6489, 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.