Information on Result #1035552
Linear OOA(4194, 109, F4, 3, 112) (dual of [(109, 3), 133, 113]-NRT-code), using construction X applied to AG(3;F,196P) ⊂ AG(3;F,205P) based on
- linear OOA(4185, 103, F4, 3, 112) (dual of [(103, 3), 124, 113]-NRT-code), using algebraic-geometric NRT-code AG(3;F,196P) [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- linear OOA(4176, 103, F4, 3, 103) (dual of [(103, 3), 133, 104]-NRT-code), using algebraic-geometric NRT-code AG(3;F,205P) [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104 (see above)
- linear OOA(49, 6, F4, 3, 8) (dual of [(6, 3), 9, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(49, 9, F4, 3, 8) (dual of [(9, 3), 18, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,18P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- extended algebraic-geometric NRT-code AGe(3;F,18P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- discarding factors / shortening the dual code based on linear OOA(49, 9, F4, 3, 8) (dual of [(9, 3), 18, 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(4194, 109, F4, 3, 111) (dual of [(109, 3), 133, 112]-NRT-code) | [i] | Strength Reduction for OOAs | |