Information on Result #1301985
Linear OA(739, 102, F7, 19) (dual of [102, 63, 20]-code), using construction X with Varšamov bound based on
- linear OA(738, 100, F7, 19) (dual of [100, 62, 20]-code), using
- trace code [i] based on linear OA(4919, 50, F49, 19) (dual of [50, 31, 20]-code or 50-arc in PG(18,49)), using
- extended Reed–Solomon code RSe(31,49) [i]
- the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- algebraic-geometric code AG(F,15P) 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]
- algebraic-geometric code AG(F,10P) with degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- algebraic-geometric code AG(F,6P) with degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- trace code [i] based on linear OA(4919, 50, F49, 19) (dual of [50, 31, 20]-code or 50-arc in PG(18,49)), using
- linear OA(738, 101, F7, 18) (dual of [101, 63, 19]-code), using Gilbert–Varšamov bound and bm = 738 > Vbs−1(k−1) = 116 484062 836107 646159 765308 578401 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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.