This paper studies skew constacyclic codes over a family of finite rings denoted by Bk to obtain quantum codes over the fields Fpr and to construct Euclidean LCD skew constacyclic codes.The author investigates the str...This paper studies skew constacyclic codes over a family of finite rings denoted by Bk to obtain quantum codes over the fields Fpr and to construct Euclidean LCD skew constacyclic codes.The author investigates the structural properties of skew constacyclic codes over Bk using a decomposition approach,and also finds necessary and sufficient conditions for skew constacyclic codes that contain their duals.Finally,the author gives some examples of quantum codes obtained via the construction and LCD codes.展开更多
We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or ...We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R.Moreover,we discuss possible extension of our results in the more general setting ofδR-dual skew constacyclic codes over R,whereδR is an automorphism of R.展开更多
文摘This paper studies skew constacyclic codes over a family of finite rings denoted by Bk to obtain quantum codes over the fields Fpr and to construct Euclidean LCD skew constacyclic codes.The author investigates the structural properties of skew constacyclic codes over Bk using a decomposition approach,and also finds necessary and sufficient conditions for skew constacyclic codes that contain their duals.Finally,the author gives some examples of quantum codes obtained via the construction and LCD codes.
基金This work was supported by the Ministry of Education and Training of Vietnam(Thai Nguyen University)under Grant No.B2019-TNA-02.
文摘We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R.Moreover,we discuss possible extension of our results in the more general setting ofδR-dual skew constacyclic codes over R,whereδR is an automorphism of R.
