Information on Result #696737
Linear OA(3270, 32784, F32, 23) (dual of [32784, 32714, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,9]) based on
- linear OA(3267, 32769, F32, 23) (dual of [32769, 32702, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(3255, 32769, F32, 19) (dual of [32769, 32714, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(3270, 24686, F32, 2, 23) (dual of [(24686, 2), 49302, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (47, 70, 24686)-net over F32 | [i] | ||
| 3 | Linear OOA(3270, 16392, F32, 2, 23) (dual of [(16392, 2), 32714, 24]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3270, 2980, F32, 23, 23) (dual of [(2980, 23), 68470, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |