Information on Result #644977
Linear OA(1627, 75, F16, 16) (dual of [75, 48, 17]-code), using construction X applied to AG(F,47P) ⊂ AG(F,53P) based on
- linear OA(1622, 64, F16, 16) (dual of [64, 42, 17]-code), using algebraic-geometric code AG(F,47P) [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(1616, 64, F16, 10) (dual of [64, 48, 11]-code), using algebraic-geometric code AG(F,53P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(165, 11, F16, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,16)), using
- discarding factors / shortening the dual code based on linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
- Reed–Solomon code RS(11,16) [i]
- discarding factors / shortening the dual code based on linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), 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(16130, 4171, F16, 37) (dual of [4171, 4041, 38]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 2 | Linear OA(16127, 4171, F16, 36) (dual of [4171, 4044, 37]-code) | [i] | ||
| 3 | Linear OA(16124, 4171, F16, 35) (dual of [4171, 4047, 36]-code) | [i] | ||
| 4 | Linear OA(16121, 4171, F16, 34) (dual of [4171, 4050, 35]-code) | [i] | ||
| 5 | Linear OOA(1627, 37, F16, 2, 16) (dual of [(37, 2), 47, 17]-NRT-code) | [i] | OOA Folding | |