Information on Result #669219
Linear OA(4943, 2457, F49, 17) (dual of [2457, 2414, 18]-code), using (u, u+v)-construction based on
- linear OA(4910, 55, F49, 8) (dual of [55, 45, 9]-code), using
- construction X applied to AG(F, Q+13P) ⊂ AG(F, Q+14P) [i] based on
- linear OA(498, 50, F49, 8) (dual of [50, 42, 9]-code or 50-arc in PG(7,49)), using algebraic-geometric code AG(F, Q+19P) with degQ = 3 and 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(495, 50, F49, 5) (dual of [50, 45, 6]-code or 50-arc in PG(4,49)), using algebraic-geometric code AG(F,22P) with degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(492, 5, F49, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- construction X applied to AG(F, Q+13P) ⊂ AG(F, Q+14P) [i] based on
- linear OA(4933, 2402, F49, 17) (dual of [2402, 2369, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
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
None.