A family of constacyclic codes over $\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}}$ and application to quantum codes
نویسندگان
چکیده
We introduce a Gray map from F2m + uF2m to F 2m 2 and study (1 + u)-constacyclic codes over F2m + uF2m ,where u 2 = 0. It is proved that the image of a (1+u)-constacyclic code length n overF2m+uF2m under the Gray map is a distance-invariant quasi-cyclic code of indexm and length 2mn over F2. We also prove that every code of length 2mnwhich is the Gray image of cyclic codes overF2m+uF2m of lengthn is permutation equivalent to a binary quasi-cyclic code of indexm. Furthermore, a family of quantum error-correcting codes obtained from the Calderbank-Shor-Steane (CSS) construction applied to (1 + u)-constacyclic codes over F2m + uF2m .
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