Information on Result #645608
Linear OA(16114, 231, F16, 71) (dual of [231, 117, 72]-code), using construction X applied to AG(F,152P) ⊂ AG(F,156P) based on
- linear OA(16111, 224, F16, 71) (dual of [224, 113, 72]-code), using algebraic-geometric code AG(F,152P) [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- linear OA(16107, 224, F16, 67) (dual of [224, 117, 68]-code), using algebraic-geometric code AG(F,156P) [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(4228, 462, F4, 71) (dual of [462, 234, 72]-code) | [i] | Trace Code | |
| 2 | Linear OOA(16114, 115, F16, 2, 71) (dual of [(115, 2), 116, 72]-NRT-code) | [i] | OOA Folding | |