Information on Result #696743
Linear OA(3234, 32784, F32, 11) (dual of [32784, 32750, 12]-code), using construction X applied to C([0,5]) ⊂ C([0,3]) based on
- linear OA(3231, 32769, F32, 11) (dual of [32769, 32738, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(3219, 32769, F32, 7) (dual of [32769, 32750, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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(3234, 32784, F32, 2, 11) (dual of [(32784, 2), 65534, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (23, 34, 32784)-net over F32 | [i] | ||
| 3 | Linear OOA(3234, 16392, F32, 2, 11) (dual of [(16392, 2), 32750, 12]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3234, 6556, F32, 11, 11) (dual of [(6556, 11), 72082, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |