Information on Result #696744
Linear OA(3228, 32784, F32, 9) (dual of [32784, 32756, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,2]) based on
- linear OA(3225, 32769, F32, 9) (dual of [32769, 32744, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(3213, 32769, F32, 5) (dual of [32769, 32756, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(323, 15, F32, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,32) or 15-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 OOA(3228, 32784, F32, 2, 9) (dual of [(32784, 2), 65540, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (19, 28, 32784)-net over F32 | [i] | ||
| 3 | Linear OOA(3228, 16392, F32, 2, 9) (dual of [(16392, 2), 32756, 10]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3228, 8195, F32, 9, 9) (dual of [(8195, 9), 73727, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |