Information on Result #659453
Linear OA(4252, 561, F4, 72) (dual of [561, 309, 73]-code), using trace code based on linear OA(6484, 187, F64, 72) (dual of [187, 103, 73]-code), using
- construction X applied to AG(F,103P) ⊂ AG(F,109P) [i] based on
- linear OA(6479, 176, F64, 72) (dual of [176, 97, 73]-code), using algebraic-geometric code AG(F,103P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- linear OA(6473, 176, F64, 66) (dual of [176, 103, 67]-code), using algebraic-geometric code AG(F,109P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177 (see above)
- linear OA(645, 11, F64, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), 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(4253, 562, F4, 72) (dual of [562, 309, 73]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4254, 563, F4, 72) (dual of [563, 309, 73]-code) | [i] | ||
| 3 | Linear OOA(4252, 280, F4, 2, 72) (dual of [(280, 2), 308, 73]-NRT-code) | [i] | OOA Folding | |