Information on Result #682576
Linear OA(5122, 15639, F5, 25) (dual of [15639, 15517, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,11]) based on
- linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(5109, 15626, F5, 23) (dual of [15626, 15517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(5123, 15640, F5, 25) (dual of [15640, 15517, 26]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5122, 11193, F5, 2, 25) (dual of [(11193, 2), 22264, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5122, 11193, F5, 3, 25) (dual of [(11193, 3), 33457, 26]-NRT-code) | [i] | ||
| 4 | Digital (97, 122, 11193)-net over F5 | [i] | ||
| 5 | Linear OOA(5122, 7819, F5, 2, 25) (dual of [(7819, 2), 15516, 26]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5122, 5213, F5, 3, 25) (dual of [(5213, 3), 15517, 26]-NRT-code) | [i] | ||
| 7 | Linear OOA(5122, 1303, F5, 25, 25) (dual of [(1303, 25), 32453, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |