Information on Result #1813803
Digital (37, 56, 699053)-net over F128, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12856, 699053, F128, 3, 19) (dual of [(699053, 3), 2097103, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12856, 2097159, F128, 19) (dual of [2097159, 2097103, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(12856, 2097160, F128, 19) (dual of [2097160, 2097104, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(12855, 2097153, F128, 19) (dual of [2097153, 2097098, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 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([0,9]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12856, 2097160, F128, 19) (dual of [2097160, 2097104, 20]-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.