Information on Result #659434
Linear OA(4237, 543, F4, 70) (dual of [543, 306, 71]-code), using trace code based on linear OA(6479, 181, F64, 70) (dual of [181, 102, 71]-code), using
- construction X applied to AG(F,105P) ⊂ AG(F,108P) [i] based on
- linear OA(6477, 176, F64, 70) (dual of [176, 99, 71]-code), using algebraic-geometric code AG(F,105P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- linear OA(6474, 176, F64, 67) (dual of [176, 102, 68]-code), using algebraic-geometric code AG(F,108P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177 (see above)
- linear OA(642, 5, F64, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), 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(4238, 544, F4, 70) (dual of [544, 306, 71]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4239, 545, F4, 70) (dual of [545, 306, 71]-code) | [i] | ||
| 3 | Linear OOA(4237, 271, F4, 2, 70) (dual of [(271, 2), 305, 71]-NRT-code) | [i] | OOA Folding | |