Information on Result #698002
Linear OA(32104, 216, F32, 59) (dual of [216, 112, 60]-code), using construction X applied to C([0,29]) ⊂ C([0,27]) based on
- linear OA(32101, 205, F32, 59) (dual of [205, 104, 60]-code), using the expurgated narrow-sense BCH-code C(I) with length 205 | 324−1, defining interval I = [0,29], and minimum distance d ≥ |{−29,−28,…,29}|+1 = 60 (BCH-bound) [i]
- linear OA(3293, 205, F32, 55) (dual of [205, 112, 56]-code), using the expurgated narrow-sense BCH-code C(I) with length 205 | 324−1, defining interval I = [0,27], and minimum distance d ≥ |{−27,−26,…,27}|+1 = 56 (BCH-bound) [i]
- linear OA(323, 11, F32, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), 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(32105, 217, F32, 59) (dual of [217, 112, 60]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(32103, 215, F32, 58) (dual of [215, 112, 59]-code) | [i] | Truncation | |
| 3 | Linear OOA(32104, 108, F32, 2, 59) (dual of [(108, 2), 112, 60]-NRT-code) | [i] | OOA Folding | |