Information on Result #1049109
Linear OOA(4242, 165, F4, 3, 85) (dual of [(165, 3), 253, 86]-NRT-code), using (u, u+v)-construction based on
- linear OOA(484, 61, F4, 3, 42) (dual of [(61, 3), 99, 43]-NRT-code), using
- construction X applied to AG(3;F,122P) ⊂ AG(3;F,131P) [i] 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(466, 55, F4, 3, 33) (dual of [(55, 3), 99, 34]-NRT-code), using algebraic-geometric NRT-code AG(3;F,131P) [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56 (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
- 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
- construction X applied to AG(3;F,122P) ⊂ AG(3;F,131P) [i] based on
- linear OOA(4158, 104, F4, 3, 85) (dual of [(104, 3), 154, 86]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,226P) [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]
- extended algebraic-geometric NRT-code AGe(3;F,226P) [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, 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(4242, 165, F4, 3, 84) (dual of [(165, 3), 253, 85]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4243, 165, F4, 3, 85) (dual of [(165, 3), 252, 86]-NRT-code) | [i] | OOA Duplication | |