We examine designs and binary codes associated with the line graph of the n-cube Qn, i.e. the Hamming graph H(n, 2). We find the automorphism groups and the parameters of the codes. We find a regular subgroup of the automorphism group that can be used for permutation decoding, or partial permutation decoding, for any information set.

We characterize the automorphism groups of quasiprimitive 2-arc-transitive graphs of twisted wreath product type. This is a partial solution for a problem of Praeger regarding quasiprimitive 2-arc transitive graphs. The solution stimulates several further research problems regarding automorphism groups of edge-transitive Cayley graphs and digraphs.

In this paper, we study the existentially closed models of the theory of partial differential fields (of characteristic zero) with an automorphism. These models are called partial differentially closed fields with an automorphism or, shorter, PDCFA. We first give a characterization of PDCFA’s in terms of differential varieties and then use this latter to obtain some algebraic properties of thes...

Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a generalization of median graphs. Just as median graphs they capture numerous properties of trees, but encompass a larger class of graphs that may be easier to recognize than the class of median graphs. We investigate the structure of tree-like partial cubes, characterize them, and provide exampl...

A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it can be embedded as an order ideal in its so-called unitization, which does have a unit. We study unitizations of GPEAs with respect to a unitizing automorphi...

BCH codes have high error correcting capability which allows classing them as good cyclic error correcting codes. This important characteristic is very useful in communication and data storage systems. Actually after almost 60 years passed from their discovery, their weights enumerators and therefore their analytical performances are known only for the lengths less than or equal to 127 and only...

We study properties of eigenvalues a matrix associated with randomly chosen partial automorphism regular rooted tree. show that asymptotically, as the level number goes to infinity, fraction non-zero converges zero in probability.