Information on Result #674622
Linear OA(3227, 177176, F3, 31) (dual of [177176, 176949, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,13]) based on
- linear OA(3221, 177148, F3, 31) (dual of [177148, 176927, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3199, 177148, F3, 27) (dual of [177148, 176949, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(36, 28, F3, 3) (dual of [28, 22, 4]-code or 28-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(3228, 177177, F3, 31) (dual of [177177, 176949, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3226, 177175, F3, 30) (dual of [177175, 176949, 31]-code) | [i] | Truncation | |
| 3 | Linear OOA(3227, 88588, F3, 2, 31) (dual of [(88588, 2), 176949, 32]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3227, 44294, F3, 4, 31) (dual of [(44294, 4), 176949, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(3227, 35435, F3, 5, 31) (dual of [(35435, 5), 176948, 32]-NRT-code) | [i] | ||