Information on Result #682866
Linear OA(5142, 3137, F5, 35) (dual of [3137, 2995, 36]-code), using construction X applied to C([0,17]) ⊂ C([0,16]) based on
- linear OA(5141, 3126, F5, 35) (dual of [3126, 2985, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(5131, 3126, F5, 33) (dual of [3126, 2995, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 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(5143, 3138, F5, 35) (dual of [3138, 2995, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5142, 3137, F5, 2, 35) (dual of [(3137, 2), 6132, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5142, 3137, F5, 3, 35) (dual of [(3137, 3), 9269, 36]-NRT-code) | [i] | ||
| 4 | Digital (107, 142, 3137)-net over F5 | [i] | ||
| 5 | Linear OA(5143, 3139, F5, 35) (dual of [3139, 2996, 36]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(5142, 1568, F5, 2, 35) (dual of [(1568, 2), 2994, 36]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(5142, 1045, F5, 3, 35) (dual of [(1045, 3), 2993, 36]-NRT-code) | [i] | ||