Information on Result #675405
Linear OA(3214, 6631, F3, 36) (dual of [6631, 6417, 37]-code), using construction X applied to C([0,18]) ⊂ C([0,13]) based on
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3145, 6562, F3, 27) (dual of [6562, 6417, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(321, 69, F3, 8) (dual of [69, 48, 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(3214, 6566, F3, 2, 36) (dual of [(6566, 2), 12918, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3214, 6566, F3, 3, 36) (dual of [(6566, 3), 19484, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(3214, 6566, F3, 4, 36) (dual of [(6566, 4), 26050, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(3214, 6566, F3, 5, 36) (dual of [(6566, 5), 32616, 37]-NRT-code) | [i] | ||
| 5 | Digital (178, 214, 6566)-net over F3 | [i] | ||