Information on Result #929294
Linear OOA(1682, 72, F16, 2, 68) (dual of [(72, 2), 62, 69]-NRT-code), using construction X applied to AG(2;F,59P) ⊂ AG(2;F,68P) based on
- linear OOA(1674, 64, F16, 2, 68) (dual of [(64, 2), 54, 69]-NRT-code), using algebraic-geometric NRT-code AG(2;F,59P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OOA(1665, 64, F16, 2, 59) (dual of [(64, 2), 63, 60]-NRT-code), using algebraic-geometric NRT-code AG(2;F,68P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OOA(168, 8, F16, 2, 8) (dual of [(8, 2), 8, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(168, 16, F16, 2, 8) (dual of [(16, 2), 24, 9]-NRT-code), using
- Reed–Solomon NRT-code RS(2;24,16) [i]
- discarding factors / shortening the dual code based on linear OOA(168, 16, F16, 2, 8) (dual of [(16, 2), 24, 9]-NRT-code), 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 OOA(4164, 144, F4, 2, 68) (dual of [(144, 2), 124, 69]-NRT-code) | [i] | Trace Code for OOAs | |