Information on Result #1048220
Linear OOA(3220, 176, F3, 3, 71) (dual of [(176, 3), 308, 72]-NRT-code), using trace code based on linear OOA(9110, 88, F9, 3, 71) (dual of [(88, 3), 154, 72]-NRT-code), using
- construction X applied to AG(3;F,159P) ⊂ AG(3;F,176P) [i] based on
- linear OOA(993, 77, F9, 3, 71) (dual of [(77, 3), 138, 72]-NRT-code), using algebraic-geometric NRT-code AG(3;F,159P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- linear OOA(976, 77, F9, 3, 54) (dual of [(77, 3), 155, 55]-NRT-code), using algebraic-geometric NRT-code AG(3;F,176P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78 (see above)
- linear OOA(917, 11, F9, 3, 16) (dual of [(11, 3), 16, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(917, 16, F9, 3, 16) (dual of [(16, 3), 31, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,31P) [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- discarding factors / shortening the dual code based on linear OOA(917, 16, F9, 3, 16) (dual of [(16, 3), 31, 17]-NRT-code), using
- linear OOA(993, 77, F9, 3, 71) (dual of [(77, 3), 138, 72]-NRT-code), using algebraic-geometric NRT-code AG(3;F,159P) [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, 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(3221, 176, F3, 3, 71) (dual of [(176, 3), 307, 72]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3220, 88, F3, 5, 71) (dual of [(88, 5), 220, 72]-NRT-code) | [i] | OOA Folding | |