A family of constacyclic codes over F_2^m+uF_2^m and application to quantum codes

12/06/2017

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by   Yongsheng Tang, et al.

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We introduce a Gray map from F_2^m+uF_2^m to F_2^2m and study (1+u)-constacyclic codes over F_2^m+uF_2^m, where u^2=0. It is proved that the image of a (1+u)-constacyclic code length n over F_2^m+uF_2^m under the Gray map is a distance-invariant quasi-cyclic code of index m and length 2mn over F_2. We also prove that every code of length 2mn which is the Gray image of cyclic codes over F_2^m+uF_2^m of length n is permutation equivalent to a binary quasi-cyclic code of index m. Furthermore, a family of quantum error-correcting codes obtained from the Calderbank-Shor-Steane (CSS) construction applied to (1+u)-constacyclic codes over F_2^m+uF_2^m.