Information on Result #660517
Linear OA(8172, 1050, F8, 52) (dual of [1050, 878, 53]-code), using trace code based on linear OA(6486, 525, F64, 52) (dual of [525, 439, 53]-code), using
- construction X applied to AG(F,459P) ⊂ AG(F,466P) [i] based on
- linear OA(6480, 512, F64, 52) (dual of [512, 432, 53]-code), using algebraic-geometric code AG(F,459P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- linear OA(6473, 512, F64, 45) (dual of [512, 439, 46]-code), using algebraic-geometric code AG(F,466P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513 (see above)
- linear OA(646, 13, F64, 6) (dual of [13, 7, 7]-code or 13-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- linear OA(6480, 512, F64, 52) (dual of [512, 432, 53]-code), using algebraic-geometric code AG(F,459P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, 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(8173, 1051, F8, 52) (dual of [1051, 878, 53]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8172, 525, F8, 2, 52) (dual of [(525, 2), 878, 53]-NRT-code) | [i] | OOA Folding | |