Information on Result #659146
Linear OA(4224, 462, F4, 69) (dual of [462, 238, 70]-code), using trace code based on linear OA(16112, 231, F16, 69) (dual of [231, 119, 70]-code), using
- construction X applied to AG(F,154P) ⊂ AG(F,158P) [i] based on
- linear OA(16109, 224, F16, 69) (dual of [224, 115, 70]-code), using algebraic-geometric code AG(F,154P) [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- linear OA(16105, 224, F16, 65) (dual of [224, 119, 66]-code), using algebraic-geometric code AG(F,158P) [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225 (see above)
- linear OA(163, 7, F16, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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(4225, 463, F4, 69) (dual of [463, 238, 70]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4224, 231, F4, 2, 69) (dual of [(231, 2), 238, 70]-NRT-code) | [i] | OOA Folding | |