We consider the characterization as well as the construction of quantum codes
that allow to transmit both quantum and classical information, which we refer
to as `hybrid codes'. We construct hybrid codes [[n,k:m,d]]q with
length n and distance d, that simultaneously transmit k qudits and m
symbols from a classical alphabet of size q. Many good codes such as
[[7,1:1,3]]2, [[9,2:2,3]]2, [[10,3:2,3]]2,
[[11,4:2,3]]2, [[11,1:2,4]]2, [[13,1:4,4]]2,
[[13,1:1,5]]2, [[14,1:2,5]]2, [[15,1:3,5]]2,
[[19,9:1,4]]2, [[20,9:2,4]]2, [[21,9:3,4]]2,
[[22,9:4,4]]2 have been found. All these codes have better parameters
than hybrid codes obtained from the best known stabilizer quantum codes.Comment: 6 page