On the $$(1+u^2+u^3)$$-Constacyclic and Cyclic Codes Over the Finite Ring $$ {F}_2+u{F}_2+u^2{F}_2+u^3{F}_2+v{F}_2 $$

Abstract

In this paper a new finite ring is introduced along with its algebraic properties. In addition, a new Gray map is defined on the ring. The Gray images of both the cyclic and the $$(1+u^{2}+u^{3})$$ -constacyclic codes over the finite ring are found to be permutation equivalent to binary quasicyclic codes. © 2019, Springer Nature Switzerland AG.