Information on Result #664828
Linear OA(16130, 4168, F16, 37) (dual of [4168, 4038, 38]-code), using (u, u+v)-construction based on
- linear OA(1627, 71, F16, 18) (dual of [71, 44, 19]-code), using
- construction X applied to AG(F,45P) ⊂ AG(F,49P) [i] based on
- linear OA(1624, 64, F16, 18) (dual of [64, 40, 19]-code), using algebraic-geometric code AG(F,45P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OA(1620, 64, F16, 14) (dual of [64, 44, 15]-code), using algebraic-geometric code AG(F,49P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(163, 7, F16, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- linear OA(1624, 64, F16, 18) (dual of [64, 40, 19]-code), using algebraic-geometric code AG(F,45P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,45P) ⊂ AG(F,49P) [i] based on
- linear OA(16103, 4097, F16, 37) (dual of [4097, 3994, 38]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (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.