U-Constacyclic codes over $${\mathbb {F}}_p+u{\mathbb {F}}_p$$ F p + u F p and their applications of constructing new non-binary quantum codes

Abstract

Structural properties of u-constacyclic codes over the ring \({\mathbb {F}}_p+u{\mathbb {F}}_p\) are given, where p is an odd prime and \(u^2=1\). Under a special Gray map from \({\mathbb {F}}_p+u{\mathbb {F}}_p\) to \({\mathbb {F}}_p^2\), some new non-binary quantum codes are obtained by this class of constacyclic codes.