Information on Result #1047583
Linear OOA(586, 44, F5, 3, 66) (dual of [(44, 3), 46, 67]-NRT-code), using construction X applied to AG(3;F,29P) ⊂ AG(3;F,31P) based on
- linear OOA(584, 42, F5, 3, 67) (dual of [(42, 3), 42, 68]-NRT-code), using algebraic-geometric NRT-code AG(3;F,29P) with degPÂ =Â 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- linear OOA(580, 42, F5, 3, 63) (dual of [(42, 3), 46, 64]-NRT-code), using algebraic-geometric NRT-code AG(3;F,31P) with degPÂ =Â 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42 (see above)
- linear OOA(52, 2, F5, 3, 2) (dual of [(2, 3), 4, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(52, 5, F5, 3, 2) (dual of [(5, 3), 13, 3]-NRT-code), using
- Reed–Solomon NRT-code RS(3;13,5) [i]
- discarding factors / shortening the dual code based on linear OOA(52, 5, F5, 3, 2) (dual of [(5, 3), 13, 3]-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(586, 44, F5, 3, 65) (dual of [(44, 3), 46, 66]-NRT-code) | [i] | Strength Reduction for OOAs | |