Information on Result #661508
Linear OA(4187, 328, F4, 67) (dual of [328, 141, 68]-code), using concatenation of two codes based on
- linear OA(6435, 82, F64, 33) (dual of [82, 47, 34]-code), using
- construction X applied to AG(F,45P) ⊂ AG(F,47P) [i] based on
- linear OA(6434, 79, F64, 33) (dual of [79, 45, 34]-code), using algebraic-geometric code AG(F,45P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- linear OA(6432, 79, F64, 31) (dual of [79, 47, 32]-code), using algebraic-geometric code AG(F,47P) [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
- construction X applied to AG(F,45P) ⊂ AG(F,47P) [i] based on
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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(4187, 328, F4, 66) (dual of [328, 141, 67]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4188, 329, F4, 67) (dual of [329, 141, 68]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4189, 330, F4, 67) (dual of [330, 141, 68]-code) | [i] | ||
| 4 | Linear OA(4190, 331, F4, 67) (dual of [331, 141, 68]-code) | [i] | ||
| 5 | Linear OA(4186, 327, F4, 66) (dual of [327, 141, 67]-code) | [i] | Truncation | |
| 6 | Linear OOA(4187, 164, F4, 2, 67) (dual of [(164, 2), 141, 68]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4187, 109, F4, 3, 67) (dual of [(109, 3), 140, 68]-NRT-code) | [i] | ||