Information on Result #928979
Linear OOA(1688, 69, F16, 2, 77) (dual of [(69, 2), 50, 78]-NRT-code), using construction X applied to AG(2;F,50P) ⊂ AG(2;F,56P) based on
- linear OOA(1683, 64, F16, 2, 77) (dual of [(64, 2), 45, 78]-NRT-code), using algebraic-geometric NRT-code AG(2;F,50P) [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(1677, 64, F16, 2, 71) (dual of [(64, 2), 51, 72]-NRT-code), using algebraic-geometric NRT-code AG(2;F,56P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OOA(165, 5, F16, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(165, 16, F16, 2, 5) (dual of [(16, 2), 27, 6]-NRT-code), using
- Reed–Solomon NRT-code RS(2;27,16) [i]
- discarding factors / shortening the dual code based on linear OOA(165, 16, F16, 2, 5) (dual of [(16, 2), 27, 6]-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(4176, 138, F4, 2, 77) (dual of [(138, 2), 100, 78]-NRT-code) | [i] | Trace Code for OOAs | |