EXTENDED ABSTRACT. Most of the results in traditional finite-field linear coding theory regarding the minimum distance of linear codes refer to the Hamming metric. Important early exceptions are given by Berlekamp’s nega-cyclic codes (cf. [1]) and Mazur’s [9] low-rate codes, both having interesting properties in terms of the Leemetric. At the beginning of the nineties of the previous century an...

For a given graph G, its line denoted by L(G) is whose vertex set V (L(G)) = E(G) and {e1, e2} ∈ E(L(G)) if e1 e2 are incident to common in G. Let R be finite commutative ring with nonzero identity G(R) denotes the unit associated R. In this manuscript, we have studied L(G(R)) of course investigation, several basic properties, viz., diameter, girth, clique, chromatic number been determined. Fur...

A module $M$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $M$ into $M$. We prove that all right (left) modules over a ring are coretractable if and only if the ring is Morita equivalent to a finite product of local right and left perfect rings.

in this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. first, we give a generalization of guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. the firs...