Simplex Codes Over the Ring\sum_ {n= 0}^ su^ n F_2

Abstract

In this paper, we introduce simplex linear codes over the ring\sum_ {n= 0}^{n= s} u^ n F_2 of types\alpha and\beta, where u^{s+ 1}= 0. And we determine their properties. These codes are an extension and generalization of simplex codes over the ring Z_ {2^ s}.