Information on Result #2277703
Linear OA(5133, 3138, F5, 33) (dual of [3138, 3005, 34]-code), using 1 times code embedding in larger space based on linear OA(5132, 3137, F5, 33) (dual of [3137, 3005, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] 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 OOA(5133, 2917, F5, 2, 33) (dual of [(2917, 2), 5701, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5133, 2917, F5, 3, 33) (dual of [(2917, 3), 8618, 34]-NRT-code) | [i] | ||
| 3 | Digital (100, 133, 2917)-net over F5 | [i] | ||
| 4 | Linear OOA(5133, 1569, F5, 2, 33) (dual of [(1569, 2), 3005, 34]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5133, 1046, F5, 3, 33) (dual of [(1046, 3), 3005, 34]-NRT-code) | [i] | ||