Information on Result #696751
Linear OA(3272, 32792, F32, 23) (dual of [32792, 32720, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,8]) 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(3249, 32769, F32, 17) (dual of [32769, 32720, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(325, 23, F32, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), 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(3272, 32792, F32, 2, 23) (dual of [(32792, 2), 65512, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (49, 72, 32792)-net over F32 | [i] | ||
| 3 | Linear OOA(3272, 16396, F32, 2, 23) (dual of [(16396, 2), 32720, 24]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3272, 2981, F32, 23, 23) (dual of [(2981, 23), 68491, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |