Information on Result #653023
Linear OA(6413, 82, F64, 11) (dual of [82, 69, 12]-code), using construction X applied to AG(F,67P) ⊂ AG(F,69P) based on
- linear OA(6412, 79, F64, 11) (dual of [79, 67, 12]-code), using algebraic-geometric code AG(F,67P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- linear OA(6410, 79, F64, 9) (dual of [79, 69, 10]-code), using algebraic-geometric code AG(F,69P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80 (see above)
- linear OA(641, 3, F64, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OA(826, 164, F8, 11) (dual of [164, 138, 12]-code) | [i] | Trace Code | |
| 2 | OA(3216, 82, S32, 11) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(6458, 4179, F64, 23) (dual of [4179, 4121, 24]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(6480, 262227, F64, 23) (dual of [262227, 262147, 24]-code) | [i] | ||
| 5 | Linear OA(6456, 4178, F64, 22) (dual of [4178, 4122, 23]-code) | [i] | ||
| 6 | Linear OA(6477, 262226, F64, 22) (dual of [262226, 262149, 23]-code) | [i] | ||
| 7 | Linear OA(6458, 4180, F64, 23) (dual of [4180, 4122, 24]-code) | [i] | ||
| 8 | Linear OA(6480, 262229, F64, 23) (dual of [262229, 262149, 24]-code) | [i] | ||
| 9 | Linear OA(6456, 4180, F64, 22) (dual of [4180, 4124, 23]-code) | [i] | ||
| 10 | Linear OA(6477, 262229, F64, 22) (dual of [262229, 262152, 23]-code) | [i] | ||
| 11 | Linear OA(6488, 262307, F64, 23) (dual of [262307, 262219, 24]-code) | [i] | (u, u−v, u+v+w)-Construction | |