Information on Result #2266635
Linear OA(3230, 19733, F3, 36) (dual of [19733, 19503, 37]-code), using 4 times code embedding in larger space based on linear OA(3226, 19729, F3, 36) (dual of [19729, 19503, 37]-code), using
- construction X applied to C([0,18]) ⊂ C([0,15]) [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(3181, 19684, F3, 31) (dual of [19684, 19503, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-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(3230, 11033, F3, 2, 36) (dual of [(11033, 2), 21836, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3230, 11033, F3, 3, 36) (dual of [(11033, 3), 32869, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(3230, 11033, F3, 4, 36) (dual of [(11033, 4), 43902, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(3230, 11033, F3, 5, 36) (dual of [(11033, 5), 54935, 37]-NRT-code) | [i] | ||
| 5 | Digital (194, 230, 11033)-net over F3 | [i] | ||