Information on Result #660029
Linear OA(830, 164, F8, 13) (dual of [164, 134, 14]-code), using trace code based on linear OA(6415, 82, F64, 13) (dual of [82, 67, 14]-code), using
- construction X applied to AG(F,65P) ⊂ AG(F,67P) [i] based on
- linear OA(6414, 79, F64, 13) (dual of [79, 65, 14]-code), using algebraic-geometric code AG(F,65P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- 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 (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(831, 165, F8, 13) (dual of [165, 134, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(830, 163, F8, 2, 13) (dual of [(163, 2), 296, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(830, 82, F8, 2, 13) (dual of [(82, 2), 134, 14]-NRT-code) | [i] | OOA Folding | |