Information on Result #644931
Linear OA(1627, 73, F16, 17) (dual of [73, 46, 18]-code), using construction X applied to AG(F,46P) ⊂ AG(F,51P) based on
- linear OA(1623, 64, F16, 17) (dual of [64, 41, 18]-code), using algebraic-geometric code AG(F,46P) [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(1618, 64, F16, 12) (dual of [64, 46, 13]-code), using algebraic-geometric code AG(F,51P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(164, 9, F16, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,16)), using
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
- Reed–Solomon code RS(12,16) [i]
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), 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(16124, 4170, F16, 35) (dual of [4170, 4046, 36]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(16121, 4169, F16, 34) (dual of [4169, 4048, 35]-code) | [i] | ||
| 3 | Linear OA(16124, 4172, F16, 35) (dual of [4172, 4048, 36]-code) | [i] | ||
| 4 | Linear OA(16121, 4172, F16, 34) (dual of [4172, 4051, 35]-code) | [i] | ||
| 5 | Linear OA(16130, 4170, F16, 37) (dual of [4170, 4040, 38]-code) | [i] | Construction X with Cyclic Codes | |
| 6 | Linear OOA(1627, 36, F16, 2, 17) (dual of [(36, 2), 45, 18]-NRT-code) | [i] | OOA Folding | |