Information on Result #698400
Linear OA(6442, 262168, F64, 13) (dual of [262168, 262126, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,3]) based on
- linear OA(6437, 262145, F64, 13) (dual of [262145, 262108, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(6419, 262145, F64, 7) (dual of [262145, 262126, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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(6442, 262168, F64, 2, 13) (dual of [(262168, 2), 524294, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6442, 262168, F64, 3, 13) (dual of [(262168, 3), 786462, 14]-NRT-code) | [i] | ||
| 3 | Digital (29, 42, 262168)-net over F64 | [i] | ||
| 4 | Linear OOA(6442, 131084, F64, 2, 13) (dual of [(131084, 2), 262126, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6442, 87389, F64, 3, 13) (dual of [(87389, 3), 262125, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(6442, 43694, F64, 13, 13) (dual of [(43694, 13), 567980, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |