Information on Result #659344
Linear OA(4195, 549, F4, 55) (dual of [549, 354, 56]-code), using trace code based on linear OA(6465, 183, F64, 55) (dual of [183, 118, 56]-code), using
- construction X applied to AG(F,120P) ⊂ AG(F,124P) [i] based on
- linear OA(6462, 176, F64, 55) (dual of [176, 114, 56]-code), using algebraic-geometric code AG(F,120P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- linear OA(6458, 176, F64, 51) (dual of [176, 118, 52]-code), using algebraic-geometric code AG(F,124P) [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(4196, 550, F4, 55) (dual of [550, 354, 56]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4197, 551, F4, 55) (dual of [551, 354, 56]-code) | [i] | ||
| 3 | Linear OOA(4195, 274, F4, 2, 55) (dual of [(274, 2), 353, 56]-NRT-code) | [i] | OOA Folding | |