A note on the Singleton bounds for codes over finite rings

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 $\frac{d(C)-1}{A}\leq n-\log_{|R|}|C|.$

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