Information on Result #697125
Linear OA(3256, 1036, F32, 27) (dual of [1036, 980, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,11]) based on
- linear OA(3253, 1025, F32, 27) (dual of [1025, 972, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3245, 1025, F32, 23) (dual of [1025, 980, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (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 | OA(1670, 1036, S16, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(3256, 661, F32, 2, 27) (dual of [(661, 2), 1266, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (29, 56, 661)-net over F32 | [i] | ||
| 4 | Linear OOA(3256, 518, F32, 2, 27) (dual of [(518, 2), 980, 28]-NRT-code) | [i] | OOA Folding | |