Information on Result #660432
Linear OA(8158, 1038, F8, 48) (dual of [1038, 880, 49]-code), using trace code based on linear OA(6479, 519, F64, 48) (dual of [519, 440, 49]-code), using
- construction X applied to AG(F,463P) ⊂ AG(F,467P) [i] based on
- linear OA(6476, 512, F64, 48) (dual of [512, 436, 49]-code), using algebraic-geometric code AG(F,463P) [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(6472, 512, F64, 44) (dual of [512, 440, 45]-code), using algebraic-geometric code AG(F,467P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513 (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
- linear OA(6476, 512, F64, 48) (dual of [512, 436, 49]-code), using algebraic-geometric code AG(F,463P) [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(8159, 1039, F8, 48) (dual of [1039, 880, 49]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8158, 519, F8, 2, 48) (dual of [(519, 2), 880, 49]-NRT-code) | [i] | OOA Folding | |