Information on Result #952330
Linear OOA(3111, 531452, F3, 3, 13) (dual of [(531452, 3), 1594245, 14]-NRT-code), using OOA 3-folding based on linear OA(3111, 1594356, F3, 13) (dual of [1594356, 1594245, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(3105, 1594324, F3, 13) (dual of [1594324, 1594219, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(379, 1594324, F3, 9) (dual of [1594324, 1594245, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(36, 32, F3, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3112, 531452, F3, 3, 13) (dual of [(531452, 3), 1594244, 14]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3110, 531451, F3, 3, 12) (dual of [(531451, 3), 1594243, 13]-NRT-code) | [i] | Truncation for OOAs | |
| 3 | Linear OOA(3111, 531452, F3, 4, 13) (dual of [(531452, 4), 2125697, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3111, 531452, F3, 5, 13) (dual of [(531452, 5), 2657149, 14]-NRT-code) | [i] | ||
| 5 | Digital (98, 111, 531452)-net over F3 | [i] | ||