Information on Result #697143
Linear OA(3278, 1042, F32, 37) (dual of [1042, 964, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,15]) based on
- linear OA(3273, 1025, F32, 37) (dual of [1025, 952, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3261, 1025, F32, 31) (dual of [1025, 964, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(325, 17, F32, 5) (dual of [17, 12, 6]-code or 17-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(3278, 902, F32, 2, 37) (dual of [(902, 2), 1726, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
2 | Digital (41, 78, 902)-net over F32 | [i] |