Information on Result #1032626
Linear OOA(497, 58, F4, 3, 60) (dual of [(58, 3), 77, 61]-NRT-code), using construction X applied to AG(3;F,104P) ⊂ AG(3;F,109P) based on
- linear OOA(493, 55, F4, 3, 60) (dual of [(55, 3), 72, 61]-NRT-code), using algebraic-geometric NRT-code AG(3;F,104P) [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(488, 55, F4, 3, 55) (dual of [(55, 3), 77, 56]-NRT-code), using algebraic-geometric NRT-code AG(3;F,109P) [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56 (see above)
- linear OOA(44, 3, F4, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(44, 4, F4, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
- Reed–Solomon NRT-code RS(3;8,4) [i]
- discarding factors / shortening the dual code based on linear OOA(44, 4, F4, 3, 4) (dual of [(4, 3), 8, 5]-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(497, 58, F4, 3, 59) (dual of [(58, 3), 77, 60]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2194, 116, F2, 3, 60) (dual of [(116, 3), 154, 61]-NRT-code) | [i] | Trace Code for OOAs | |