A note on the Singleton bounds for codes over finite rings (1611.09058v1)

Abstract: In this paper, we give a notation on the Singleton bounds for linear codes over a finite commutative quasi-Frobenius ring in the work of Shiromoto [5]. We show that there exists a class of finite commutative quasi-Frobenius rings. The Singleton bounds for linear codes over such rings satisfy [ \frac{d(C)-1}{A}\leq n-\log_{|R|}|C|. ]