Information on Result #1301680
Linear OA(5104, 390667, F5, 15) (dual of [390667, 390563, 16]-code), using construction X with Varšamov bound 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, 390665, F5, 14) (dual of [390665, 390563, 15]-code), using Gilbert–Varšamov bound and bm = 5102 > Vbs−1(k−1) = 53193 745862 602493 797430 379791 679157 443033 533989 863981 139672 422088 711649 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(5104, 390667, F5, 2, 15) (dual of [(390667, 2), 781230, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5104, 390667, F5, 3, 15) (dual of [(390667, 3), 1171897, 16]-NRT-code) | [i] | ||
| 3 | Digital (89, 104, 390667)-net over F5 | [i] | ||
| 4 | Linear OOA(5104, 195333, F5, 2, 15) (dual of [(195333, 2), 390562, 16]-NRT-code) | [i] | OOA Folding | |