Let p $p$ be a fixed prime. We show that the number of isomorphism classes finite rings order n $p^n$ is α $p^\alpha$ , where = 4 27 3 + O ( 5 / 2 ) $\alpha =\frac{4}{27}n^3+\mathnormal {O}(n^{5/2})$ . This result was stated (with weaker error term) by Kruse and Price in 1969; problem with their proof pointed out Knopfmacher 1973. also commutative β $p^\beta$ $\beta =\frac{2}{27}n^3+\mathnormal...

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...