Information on Result #682248
Linear OA(5141, 390686, F5, 20) (dual of [390686, 390545, 21]-code), using construction X applied to C([0,10]) ⊂ C([0,6]) based on
- linear OA(5129, 390626, F5, 21) (dual of [390626, 390497, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(581, 390626, F5, 13) (dual of [390626, 390545, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(512, 60, F5, 6) (dual of [60, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
Mode: Constructive and 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 OA(5142, 390687, F5, 20) (dual of [390687, 390545, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5141, 390686, F5, 2, 20) (dual of [(390686, 2), 781231, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5141, 390686, F5, 3, 20) (dual of [(390686, 3), 1171917, 21]-NRT-code) | [i] | ||
| 4 | Digital (121, 141, 390686)-net over F5 | [i] | ||
| 5 | Linear OA(5142, 390688, F5, 20) (dual of [390688, 390546, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(5143, 390690, F5, 20) (dual of [390690, 390547, 21]-code) | [i] | ||
| 7 | Linear OOA(5141, 195343, F5, 2, 20) (dual of [(195343, 2), 390545, 21]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(5141, 130228, F5, 3, 20) (dual of [(130228, 3), 390543, 21]-NRT-code) | [i] | ||
| 9 | Linear OOA(5141, 39068, F5, 20, 20) (dual of [(39068, 20), 781219, 21]-NRT-code) | [i] | OA Folding and Stacking | |