Information on Result #659264
Linear OA(4138, 318, F4, 42) (dual of [318, 180, 43]-code), using trace code based on linear OA(6446, 106, F64, 42) (dual of [106, 60, 43]-code), using
- construction X applied to AG(F,60P) ⊂ AG(F,62P) [i] based on
- linear OA(6445, 103, F64, 42) (dual of [103, 58, 43]-code), using algebraic-geometric code AG(F,60P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- linear OA(6443, 103, F64, 40) (dual of [103, 60, 41]-code), using algebraic-geometric code AG(F,62P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104 (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(4139, 319, F4, 42) (dual of [319, 180, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4140, 320, F4, 42) (dual of [320, 180, 43]-code) | [i] | ||
| 3 | Linear OOA(4138, 159, F4, 2, 42) (dual of [(159, 2), 180, 43]-NRT-code) | [i] | OOA Folding | |