Information on Result #658999
Linear OA(16115, 138, F16, 77) (dual of [138, 23, 78]-code), using repeating each code word 2 times based on linear OA(1646, 69, F16, 38) (dual of [69, 23, 39]-code), using
- construction X applied to AG(F,25P) ⊂ AG(F,28P) [i] based on
- linear OA(1644, 64, F16, 38) (dual of [64, 20, 39]-code), using algebraic-geometric code AG(F,25P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OA(1641, 64, F16, 35) (dual of [64, 23, 36]-code), using algebraic-geometric code AG(F,28P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(162, 5, F16, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- linear OA(1644, 64, F16, 38) (dual of [64, 20, 39]-code), using algebraic-geometric code AG(F,25P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, 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(16115, 138, F16, 76) (dual of [138, 23, 77]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(16114, 137, F16, 76) (dual of [137, 23, 77]-code) | [i] | Truncation | |
| 3 | Linear OOA(16115, 69, F16, 2, 77) (dual of [(69, 2), 23, 78]-NRT-code) | [i] | OOA Folding | |