Information on Result #659988
Linear OA(728, 106, F7, 13) (dual of [106, 78, 14]-code), using trace code based on linear OA(4914, 53, F49, 13) (dual of [53, 39, 14]-code), using
- construction X applied to AG(F,18P) ⊂ AG(F,19P) [i] based on
- linear OA(4913, 50, F49, 13) (dual of [50, 37, 14]-code or 50-arc in PG(12,49)), using algebraic-geometric code AG(F,18P) with degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
- linear OA(4911, 50, F49, 11) (dual of [50, 39, 12]-code or 50-arc in PG(10,49)), using algebraic-geometric code AG(F,19P) with degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(491, 3, F49, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) 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 OA(729, 107, F7, 13) (dual of [107, 78, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(728, 53, F7, 2, 13) (dual of [(53, 2), 78, 14]-NRT-code) | [i] | OOA Folding | |