Information on Result #698528
Linear OA(6441, 262163, F64, 13) (dual of [262163, 262122, 14]-code), using construction X applied to Ce(12) ⊂ Ce(7) based on
- linear OA(6437, 262144, F64, 13) (dual of [262144, 262107, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), 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(6441, 262163, F64, 2, 13) (dual of [(262163, 2), 524285, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6441, 262163, F64, 3, 13) (dual of [(262163, 3), 786448, 14]-NRT-code) | [i] | ||
| 3 | Digital (28, 41, 262163)-net over F64 | [i] | ||
| 4 | Linear OOA(6441, 131081, F64, 2, 13) (dual of [(131081, 2), 262121, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6441, 87387, F64, 3, 13) (dual of [(87387, 3), 262120, 14]-NRT-code) | [i] | ||