Quantum codes from (1+βu)-constacyclic codes over Fpm+uFpm

Abstract

In this paper quantum codes over Fm are constructed from self-orthogonal (1+β u)-constacyclic codes of length N=nps over R=Fpm+uFpm, u2=0, where p is an odd prime, (n, \ p)=1, and β is a non-zero element of Fpm. To obtain such quantum codes, the algebraic structure of (1+β u)-constacyclic codes of length N over R is studied. The structure of their duals is also determined. From the algebraic structures of the (1+β u)-constacyclic codes and their duals over R, self-orthogonal codes over Fpm are obtained as Gray images of self-orthogonal codes over R. Then applying the CalderbankShor-Steane (CSS) construction to these self-orthogonal codes over Fpm, the parameters of the corresponding quantum codes are determined. An example is given to illustrate the results.