Information on Result #1033114
Linear OOA(487, 63, F4, 3, 42) (dual of [(63, 3), 102, 43]-NRT-code), using construction X applied to AG(3;F,122P) ⊂ AG(3;F,134P) based on
- linear OOA(475, 55, F4, 3, 42) (dual of [(55, 3), 90, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,122P) [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- linear OOA(463, 55, F4, 3, 30) (dual of [(55, 3), 102, 31]-NRT-code), using algebraic-geometric NRT-code AG(3;F,134P) [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56 (see above)
- linear OOA(412, 8, F4, 3, 11) (dual of [(8, 3), 12, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(412, 9, F4, 3, 11) (dual of [(9, 3), 15, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,15P) [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,15P) [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(412, 9, F4, 3, 11) (dual of [(9, 3), 15, 12]-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(4244, 167, F4, 3, 84) (dual of [(167, 3), 257, 85]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(4245, 167, F4, 3, 85) (dual of [(167, 3), 256, 86]-NRT-code) | [i] | ||