Information on Result #735098
Linear OA(6443, 262212, F64, 13) (dual of [262212, 262169, 14]-code), using (u, u+v)-construction based on
- linear OA(646, 65, F64, 6) (dual of [65, 59, 7]-code or 65-arc in PG(5,64)), using
- extended Reed–Solomon code RSe(59,64) [i]
- linear OA(6437, 262147, F64, 13) (dual of [262147, 262110, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] 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(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(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
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(6443, 262212, F64, 2, 13) (dual of [(262212, 2), 524381, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6443, 262212, F64, 3, 13) (dual of [(262212, 3), 786593, 14]-NRT-code) | [i] | ||
| 3 | Digital (30, 43, 262212)-net over F64 | [i] | ||
| 4 | Linear OOA(6443, 131106, F64, 2, 13) (dual of [(131106, 2), 262169, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6443, 87404, F64, 3, 13) (dual of [(87404, 3), 262169, 14]-NRT-code) | [i] | ||