Information on Result #1034559
Linear OOA(4138, 73, F4, 3, 77) (dual of [(73, 3), 81, 78]-NRT-code), using construction X applied to AG(3;F,117P) ⊂ AG(3;F,129P) based on
- linear OOA(4126, 65, F4, 3, 77) (dual of [(65, 3), 69, 78]-NRT-code), using algebraic-geometric NRT-code AG(3;F,117P) [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- linear OOA(4114, 65, F4, 3, 65) (dual of [(65, 3), 81, 66]-NRT-code), using algebraic-geometric NRT-code AG(3;F,129P) [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66 (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(4138, 73, F4, 3, 76) (dual of [(73, 3), 81, 77]-NRT-code) | [i] | Strength Reduction for OOAs | |