Information on Result #1722638
Digital (88, 103, 130221)-net over F5, using net defined by OOA based on linear OOA(5103, 130221, F5, 21, 15) (dual of [(130221, 21), 2734538, 16]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(5103, 390664, F5, 3, 15) (dual of [(390664, 3), 1171889, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5103, 390665, F5, 3, 15) (dual of [(390665, 3), 1171892, 16]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5103, 390665, F5, 15) (dual of [390665, 390562, 16]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5102, 390663, F5, 15) (dual of [390663, 390561, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(597, 390626, F5, 15) (dual of [390626, 390529, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(565, 390626, F5, 11) (dual of [390626, 390561, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(55, 37, F5, 3) (dual of [37, 32, 4]-code or 37-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(5102, 390664, F5, 14) (dual of [390664, 390562, 15]-code), using Gilbert–Varšamov bound and bm = 5102 > Vbs−1(k−1) = 53191 975752 600882 847800 129453 853790 460514 506906 867017 436994 682898 561325 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(5102, 390663, F5, 15) (dual of [390663, 390561, 16]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5103, 390665, F5, 15) (dual of [390665, 390562, 16]-code), using
- discarding factors / shortening the dual code based on linear OOA(5103, 390665, F5, 3, 15) (dual of [(390665, 3), 1171892, 16]-NRT-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.