Information on Result #674461
Linear OA(3247, 531472, F3, 31) (dual of [531472, 531225, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,13]) based on
- linear OA(3241, 531442, F3, 31) (dual of [531442, 531201, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3217, 531442, F3, 27) (dual of [531442, 531225, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(36, 30, F3, 3) (dual of [30, 24, 4]-code or 30-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 OA(3248, 531473, F3, 31) (dual of [531473, 531225, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3246, 531471, F3, 30) (dual of [531471, 531225, 31]-code) | [i] | Truncation | |
| 3 | Linear OOA(3247, 265736, F3, 2, 31) (dual of [(265736, 2), 531225, 32]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3247, 177157, F3, 3, 31) (dual of [(177157, 3), 531224, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(3247, 132868, F3, 4, 31) (dual of [(132868, 4), 531225, 32]-NRT-code) | [i] | ||