Information on Result #698405
Linear OA(6468, 262176, F64, 21) (dual of [262176, 262108, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,6]) based on
- linear OA(6461, 262145, F64, 21) (dual of [262145, 262084, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 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(647, 31, F64, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), 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(6468, 262176, F64, 2, 21) (dual of [(262176, 2), 524284, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6468, 262176, F64, 3, 21) (dual of [(262176, 3), 786460, 22]-NRT-code) | [i] | ||
| 3 | Digital (47, 68, 262176)-net over F64 | [i] | ||
| 4 | Linear OOA(6468, 131088, F64, 2, 21) (dual of [(131088, 2), 262108, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6468, 87392, F64, 3, 21) (dual of [(87392, 3), 262108, 22]-NRT-code) | [i] | ||