Information on Result #698399
Linear OA(6448, 262168, F64, 15) (dual of [262168, 262120, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,4]) based on
- linear OA(6443, 262145, F64, 15) (dual of [262145, 262102, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(6425, 262145, F64, 9) (dual of [262145, 262120, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(645, 23, F64, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), 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 | Linear OOA(6448, 262168, F64, 2, 15) (dual of [(262168, 2), 524288, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6448, 262168, F64, 3, 15) (dual of [(262168, 3), 786456, 16]-NRT-code) | [i] | ||
| 3 | Digital (33, 48, 262168)-net over F64 | [i] | ||
| 4 | Linear OOA(6448, 131084, F64, 2, 15) (dual of [(131084, 2), 262120, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6448, 87389, F64, 3, 15) (dual of [(87389, 3), 262119, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(6448, 37452, F64, 15, 15) (dual of [(37452, 15), 561732, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |