Information on Result #644787
Linear OA(1624, 67, F16, 17) (dual of [67, 43, 18]-code), using construction X applied to AG(F,46P) ⊂ AG(F,48P) 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(1621, 64, F16, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 3, F16, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(448, 134, F4, 17) (dual of [134, 86, 18]-code) | [i] | Trace Code | |
| 2 | Linear OA(1694, 581, F16, 35) (dual of [581, 487, 36]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(16121, 4164, F16, 35) (dual of [4164, 4043, 36]-code) | [i] | ||
| 4 | Linear OA(1692, 581, F16, 34) (dual of [581, 489, 35]-code) | [i] | ||
| 5 | Linear OA(16118, 4163, F16, 34) (dual of [4163, 4045, 35]-code) | [i] | ||
| 6 | Linear OA(16121, 4166, F16, 35) (dual of [4166, 4045, 36]-code) | [i] | ||
| 7 | Linear OA(16122, 4171, F16, 35) (dual of [4171, 4049, 36]-code) | [i] | ||
| 8 | Linear OA(16118, 4166, F16, 34) (dual of [4166, 4048, 35]-code) | [i] | ||
| 9 | Linear OA(16120, 4171, F16, 34) (dual of [4171, 4051, 35]-code) | [i] | ||
| 10 | Linear OA(16121, 4175, F16, 34) (dual of [4175, 4054, 35]-code) | [i] | ||
| 11 | Linear OA(16127, 4164, F16, 37) (dual of [4164, 4037, 38]-code) | [i] | Construction X with Cyclic Codes | |
| 12 | Linear OOA(1624, 33, F16, 2, 17) (dual of [(33, 2), 42, 18]-NRT-code) | [i] | OOA Folding | |