Information on Result #682867
Linear OA(5132, 3137, F5, 33) (dual of [3137, 3005, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,15]) based on
- 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(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (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(5133, 3138, F5, 33) (dual of [3138, 3005, 34]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5134, 3139, F5, 33) (dual of [3139, 3005, 34]-code) | [i] | ||
| 3 | Linear OOA(5132, 2769, F5, 2, 33) (dual of [(2769, 2), 5406, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(5132, 2769, F5, 3, 33) (dual of [(2769, 3), 8175, 34]-NRT-code) | [i] | ||
| 5 | Digital (99, 132, 2769)-net over F5 | [i] | ||
| 6 | Linear OA(5134, 3140, F5, 33) (dual of [3140, 3006, 34]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(5132, 1568, F5, 2, 33) (dual of [(1568, 2), 3004, 34]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(5132, 1045, F5, 3, 33) (dual of [(1045, 3), 3003, 34]-NRT-code) | [i] | ||