Information on Result #1782521
Digital (196, 231, 65624)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4231, 65624, F4, 35) (dual of [65624, 65393, 36]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4230, 65622, F4, 35) (dual of [65622, 65392, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,12]) [i] based on
- linear OA(4209, 65537, F4, 35) (dual of [65537, 65328, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(421, 85, F4, 9) (dual of [85, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 86, F4, 9) (dual of [86, 65, 10]-code), using
- construction X applied to C([0,17]) ⊂ C([0,12]) [i] based on
- linear OA(4230, 65623, F4, 34) (dual of [65623, 65393, 35]-code), using Gilbert–Varšamov bound and bm = 4230 > Vbs−1(k−1) = 582808 498161 634596 259000 790155 291164 431501 810811 926889 480294 559696 490655 286417 870666 072168 823004 908903 028331 039449 429569 576119 540677 825862 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4230, 65622, F4, 35) (dual of [65622, 65392, 36]-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.