Information on Result #938029
Linear OOA(542, 44, F5, 2, 23) (dual of [(44, 2), 46, 24]-NRT-code), using construction X applied to AG(2;F,30P) ⊂ AG(2;F,31P) based on
- linear OOA(540, 42, F5, 2, 23) (dual of [(42, 2), 44, 24]-NRT-code), using algebraic-geometric NRT-code AG(2;F,30P) 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(538, 42, F5, 2, 21) (dual of [(42, 2), 46, 22]-NRT-code), using algebraic-geometric NRT-code AG(2;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, 2, 1) (dual of [(2, 2), 2, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(52, s, F5, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(52, s, F5, 1) (dual of [s, s−2, 2]-code) for arbitrarily large s, using
- 51 times duplication / taking a subcode [i] based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(52, s, F5, 1) (dual of [s, s−2, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(52, s, F5, 2, 1) for arbitrarily large s, 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(542, 22, F5, 3, 23) (dual of [(22, 3), 24, 24]-NRT-code) | [i] | OOA Folding | |