A family of constacyclic codes over F2 + uF2 + vF2 + uvF2

This paper studies (1 + u)-constacyclic codes over the ring F2 + uF2 + vF2 + uvF2. It is proved that the image of a (1+u)-constacyclic code of length n over F2+uF2+vF2+uvF2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is determined. Some optimal binary codes are obtained directly from (1 + u)-constacyclic codes over F2 + uF2 + vF2 + uvF2.

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