Information on Result #732074
Linear OA(16113, 1048648, F16, 21) (dual of [1048648, 1048535, 22]-code), using (u, u+v)-construction based on
- linear OA(1617, 67, F16, 10) (dual of [67, 50, 11]-code), using
- construction X applied to AG(F,53P) ⊂ AG(F,55P) [i] based on
- linear OA(1616, 64, F16, 10) (dual of [64, 48, 11]-code), using algebraic-geometric code AG(F,53P) [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(1614, 64, F16, 8) (dual of [64, 50, 9]-code), using algebraic-geometric code AG(F,55P) [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(1616, 64, F16, 10) (dual of [64, 48, 11]-code), using algebraic-geometric code AG(F,53P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,53P) ⊂ AG(F,55P) [i] based on
- linear OA(1696, 1048581, F16, 21) (dual of [1048581, 1048485, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [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.