Information on Result #1163781
Linear OOA(2243, 61, F2, 7, 122) (dual of [(61, 7), 184, 123]-NRT-code), using construction X applied to AG(7;F,106P) ⊂ AG(7;F,127P) based on
- linear OOA(2192, 48, F2, 7, 123) (dual of [(48, 7), 144, 124]-NRT-code), using algebraic-geometric NRT-code AG(7;F,106P) with degPÂ =Â 2 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- linear OOA(2150, 48, F2, 7, 81) (dual of [(48, 7), 186, 82]-NRT-code), using algebraic-geometric NRT-code AG(7;F,127P) with degPÂ =Â 2 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48 (see above)
- linear OOA(251, 13, F2, 7, 40) (dual of [(13, 7), 40, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(251, 14, F2, 7, 40) (dual of [(14, 7), 47, 41]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(7;F,57P) [i] based on function field F/F2 with g(F) = 11 and N(F) ≥ 14, using
- discarding factors / shortening the dual code based on linear OOA(251, 14, F2, 7, 40) (dual of [(14, 7), 47, 41]-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(2243, 61, F2, 7, 121) (dual of [(61, 7), 184, 122]-NRT-code) | [i] | Strength Reduction for OOAs | |