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 $$\frac{d(C)-1}{A}\le n-{\log }_{\mathrm{\mid }R\mathrm{\mid }}\mathrm{\mid }C\mathrm{\mid }\mathrm{.}$$