Information on Result #659289
Linear OA(4162, 549, F4, 44) (dual of [549, 387, 45]-code), using trace code based on linear OA(6454, 183, F64, 44) (dual of [183, 129, 45]-code), using
- construction X applied to AG(F,131P) ⊂ AG(F,135P) [i] based on
- linear OA(6451, 176, F64, 44) (dual of [176, 125, 45]-code), using algebraic-geometric code AG(F,131P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- linear OA(6447, 176, F64, 40) (dual of [176, 129, 41]-code), using algebraic-geometric code AG(F,135P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177 (see above)
- linear OA(643, 7, F64, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,64) or 7-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), 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(4163, 550, F4, 44) (dual of [550, 387, 45]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4164, 551, F4, 44) (dual of [551, 387, 45]-code) | [i] | ||
| 3 | Linear OOA(4162, 274, F4, 2, 44) (dual of [(274, 2), 386, 45]-NRT-code) | [i] | OOA Folding | |