Information on Result #1814057
Digital (45, 68, 699053)-net over F128, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12868, 699053, F128, 3, 23) (dual of [(699053, 3), 2097091, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12868, 2097159, F128, 23) (dual of [2097159, 2097091, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12868, 2097160, F128, 23) (dual of [2097160, 2097092, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(12867, 2097153, F128, 23) (dual of [2097153, 2097086, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(12861, 2097153, F128, 21) (dual of [2097153, 2097092, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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([0,11]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12868, 2097160, F128, 23) (dual of [2097160, 2097092, 24]-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.