Information on Result #691989
Linear OA(16127, 4164, F16, 37) (dual of [4164, 4037, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,9]) 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]
- linear OA(1655, 4097, F16, 19) (dual of [4097, 4042, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(1624, 67, F16, 17) (dual of [67, 43, 18]-code), using
- construction X applied to AG(F,46P) ⊂ AG(F,48P) [i] based on
- linear OA(1623, 64, F16, 17) (dual of [64, 41, 18]-code), using algebraic-geometric code AG(F,46P) [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(1621, 64, F16, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 3, F16, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(1623, 64, F16, 17) (dual of [64, 41, 18]-code), using algebraic-geometric code AG(F,46P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,46P) ⊂ AG(F,48P) [i] based on
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.