New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codes

Abstract

In this paper, some families of asymmetric quantum codes and quantum convolutional codes that satisfy the quantum Singleton bound are constructed by utilizing constacyclic codes with length $$n=\frac{q^2+1}{10h}$$ , where q is an odd prime power with the form $$q=10hm+t$$ or $$q=10hm+10h-t$$ , where m is a positive integer, and both h and t are odd with $$10h=t^2+1$$ and $$t\ge 3$$ . Compared with those codes constructed in the literature, the parameters of these constructed quantum codes in this paper are more general. Moreover, the distance $$d_z$$ of optimal asymmetric quantum codes $$[[n,k,d_z/d_x]]_{q^2}$$ here is larger than most of the ones given in the literature.