Information on Result #2266638
Linear OA(3239, 19760, F3, 36) (dual of [19760, 19521, 37]-code), using 1 times code embedding in larger space based on linear OA(3238, 19759, F3, 36) (dual of [19759, 19521, 37]-code), using
- construction X applied to C([0,18]) ⊂ C([0,13]) [i] based on
- linear OA(3217, 19684, F3, 37) (dual of [19684, 19467, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3163, 19684, F3, 27) (dual of [19684, 19521, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(321, 75, F3, 8) (dual of [75, 54, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-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 OOA(3239, 14768, F3, 2, 36) (dual of [(14768, 2), 29297, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3239, 14768, F3, 3, 36) (dual of [(14768, 3), 44065, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(3239, 14768, F3, 4, 36) (dual of [(14768, 4), 58833, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(3239, 14768, F3, 5, 36) (dual of [(14768, 5), 73601, 37]-NRT-code) | [i] | ||
| 5 | Digital (203, 239, 14768)-net over F3 | [i] | ||
| 6 | Linear OOA(3239, 9880, F3, 2, 36) (dual of [(9880, 2), 19521, 37]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3239, 4940, F3, 4, 36) (dual of [(4940, 4), 19521, 37]-NRT-code) | [i] | ||
| 8 | Linear OOA(3239, 3952, F3, 5, 36) (dual of [(3952, 5), 19521, 37]-NRT-code) | [i] | ||