Information on Result #660318
Linear OA(8140, 382, F8, 56) (dual of [382, 242, 57]-code), using trace code based on linear OA(6470, 191, F64, 56) (dual of [191, 121, 57]-code), using
- construction X applied to AG(F,119P) ⊂ AG(F,127P) [i] based on
- linear OA(6463, 176, F64, 56) (dual of [176, 113, 57]-code), using algebraic-geometric code AG(F,119P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- linear OA(6455, 176, F64, 48) (dual of [176, 121, 49]-code), using algebraic-geometric code AG(F,127P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177 (see above)
- linear OA(647, 15, F64, 7) (dual of [15, 8, 8]-code or 15-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), 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(8141, 383, F8, 56) (dual of [383, 242, 57]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8140, 191, F8, 2, 56) (dual of [(191, 2), 242, 57]-NRT-code) | [i] | OOA Folding | |