Information on Result #698537
Linear OA(6457, 262167, F64, 18) (dual of [262167, 262110, 19]-code), using construction X applied to Ce(17) ⊂ Ce(11) based on
- linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(6457, 226368, F64, 2, 18) (dual of [(226368, 2), 452679, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6457, 226368, F64, 3, 18) (dual of [(226368, 3), 679047, 19]-NRT-code) | [i] | ||
| 3 | Digital (39, 57, 226368)-net over F64 | [i] | ||
| 4 | Linear OOA(6457, 131083, F64, 2, 18) (dual of [(131083, 2), 262109, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6457, 87389, F64, 3, 18) (dual of [(87389, 3), 262110, 19]-NRT-code) | [i] | ||