Information on Result #698406
Linear OA(6462, 262176, F64, 19) (dual of [262176, 262114, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,5]) based on
- linear OA(6455, 262145, F64, 19) (dual of [262145, 262090, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(6431, 262145, F64, 11) (dual of [262145, 262114, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(6462, 262176, F64, 2, 19) (dual of [(262176, 2), 524290, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6462, 262176, F64, 3, 19) (dual of [(262176, 3), 786466, 20]-NRT-code) | [i] | ||
| 3 | Digital (43, 62, 262176)-net over F64 | [i] | ||
| 4 | Linear OOA(6462, 131088, F64, 2, 19) (dual of [(131088, 2), 262114, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6462, 87392, F64, 3, 19) (dual of [(87392, 3), 262114, 20]-NRT-code) | [i] | ||