Information on Result #696759
Linear OA(3298, 32800, F32, 31) (dual of [32800, 32702, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,11]) based on
- linear OA(3291, 32769, F32, 31) (dual of [32769, 32678, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 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(327, 31, F32, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,32)), using
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), 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(3299, 32801, F32, 31) (dual of [32801, 32702, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3298, 32800, F32, 2, 31) (dual of [(32800, 2), 65502, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (67, 98, 32800)-net over F32 | [i] | ||
| 4 | Linear OOA(3298, 16400, F32, 2, 31) (dual of [(16400, 2), 32702, 32]-NRT-code) | [i] | OOA Folding | |