Information on Result #735135
Linear OA(6429, 262212, F64, 9) (dual of [262212, 262183, 10]-code), using (u, u+v)-construction based on
- linear OA(644, 65, F64, 4) (dual of [65, 61, 5]-code or 65-arc in PG(3,64)), using
- extended Reed–Solomon code RSe(61,64) [i]
- linear OA(6425, 262147, F64, 9) (dual of [262147, 262122, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(6425, 262144, F64, 9) (dual of [262144, 262119, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(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(8) ⊂ Ce(7) [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(6429, 262212, F64, 2, 9) (dual of [(262212, 2), 524395, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6429, 262212, F64, 3, 9) (dual of [(262212, 3), 786607, 10]-NRT-code) | [i] | ||
| 3 | Digital (20, 29, 262212)-net over F64 | [i] | ||
| 4 | Linear OOA(6429, 131106, F64, 2, 9) (dual of [(131106, 2), 262183, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6429, 87404, F64, 3, 9) (dual of [(87404, 3), 262183, 10]-NRT-code) | [i] | ||