Information on Result #698661
Linear OA(6482, 4126, F64, 37) (dual of [4126, 4044, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,13]) based on
- linear OA(6473, 4097, F64, 37) (dual of [4097, 4024, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(6453, 4097, F64, 27) (dual of [4097, 4044, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(649, 29, F64, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,64)), using
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
- Reed–Solomon code RS(55,64) [i]
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), 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(3299, 4126, S32, 37) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6482, 3325, F64, 2, 37) (dual of [(3325, 2), 6568, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6482, 3325, F64, 3, 37) (dual of [(3325, 3), 9893, 38]-NRT-code) | [i] | ||
| 4 | Digital (45, 82, 3325)-net over F64 | [i] | ||
| 5 | Linear OOA(6482, 2063, F64, 2, 37) (dual of [(2063, 2), 4044, 38]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6482, 1375, F64, 3, 37) (dual of [(1375, 3), 4043, 38]-NRT-code) | [i] | ||