Information on Result #919428
Linear OOA(497, 64, F4, 2, 55) (dual of [(64, 2), 31, 56]-NRT-code), using construction X applied to AG(2;F,54P) ⊂ AG(2;F,63P) based on
- linear OOA(488, 55, F4, 2, 55) (dual of [(55, 2), 22, 56]-NRT-code), using algebraic-geometric NRT-code AG(2;F,54P) [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(479, 55, F4, 2, 46) (dual of [(55, 2), 31, 47]-NRT-code), using algebraic-geometric NRT-code AG(2;F,63P) [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56 (see above)
- linear OOA(49, 9, F4, 2, 8) (dual of [(9, 2), 9, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,9P) [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(2;F,9P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, 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(497, 64, F4, 2, 54) (dual of [(64, 2), 31, 55]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(499, 65, F4, 2, 55) (dual of [(65, 2), 31, 56]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |