Related papers: Alphabet-Almost-Simple 2-Neighbour Transitive Code…

Non-trivial $2$-$(k^{2},k,\lambda )$ designs, with $\lambda \mid k$, admitting a flag-transitive almost simple automorphism group are classified.

A graph is edge-primitive if its automorphism group acts primitively on the edge set. In this short paper, we prove that a finite 2-arc-transitive edge-primitive graph has almost simple automorphism group if it is neither a cycle nor a…

In this paper we present a geometrical characterization for the minimum-weight codewords of the Hermitian codes over the fields $\mathbb{F}_{q^2}$ in the third and fourth phase, namely with distance $d \geq q^2-q$. We consider the unique…

Let $\Gamma$ denote a $Q$-polynomial distance-regular graph with vertex set $X$ and diameter $D$. Let $A$ denote the adjacency matrix of $\Gamma$. For a vertex $x\in X$ and for $0 \leq i \leq D$, let $E^*_i(x)$ denote the projection matrix…

The setting of projective systems can be used to study the parameters of a projective linear code $\mathcal{C}$. This can be done by considering the intersections of the point set $\Omega$ defined by the columns of a generating matrix for…

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two…

This paper is devoted to the study of $2$-designs with $\lambda\ge (r,\lambda)^2$ admitting a flag-transitive automorphism group $G$. The group $G$ has been shown to be point-primitive of either almost simple or affine type. In this paper,…

Given $k\ge 2$ and two $k$-graphs ($k$-uniform hypergraphs) $F$ and $H$, an \emph{$F$-factor} in $H$ is a set of vertex disjoint copies of $F$ that together covers the vertex set of $H$. Lenz and Mubayi studied the $F$-factor problems in…

We study the cohomology of symbolic dynamical systems called homshifts: they are the nearest-neighbour $\mathbb{Z}^d$ shifts of finite type whose adjacency rules are the same in every direction. Building on the work of Klaus Schmidt…

Let X be a projective complex 3-fold, quasihomogeneous with respect to an action of a linear algebraic group. We show that X is a compactification of SL_2/G, G a discrete subgroup, or that X can be equivariantly transformed into the 3-dim.…

Let $\mathcal{F}$ and $\mathcal{G}$ be two $t$-uniform families of subsets over $[k] = \{1,2,...,k\}$, where $|\mathcal{F}| = |\mathcal{G}|$, and let $C$ be the adjacency matrix of the bipartite graph whose vertices are the subsets in…

The \emph{Hamming distance} $\text{ham}(u,v)$ between two equal-length words $u$, $v$ is the number of positions where $u$ and $v$ differ. The words $u$ and $v$ are said to be \emph{conjugates} if there exist non-empty words $x,y$ such that…

A half-arc-transitive graph is a regular graph that is both vertex- and edge-transitive, but is not arc-transitive. If such a graph has finite valency, then its valency is even, and greater than $2$. In 1970, Bouwer proved that there exists…

A flag is a sequence of nested subspaces of a given ambient space F_q^n over a finite field F_q. In network coding, a flag code is a set of flags, all of them with the same sequence of dimensions, the type vector. In this paper, we…

Let $H$ be a subnormal co-compact closed subgroup of a Hausdorff topological group $T$ and $X$ a compact Hausdorff space. We prove the inheritance theorem: A point of $X$ is almost periodic (a.p.) for $T\curvearrowright X$ iff it is a.p.…

An action of a group $G$ on a set $X$ is said to be quasi-n-transitive if the diagonal action of $G$ on $X^n$ has only finitely many orbits. We show that branch groups, a special class of groups of automorphisms of rooted trees, cannot act…

This paper begins the classification of all edge-primitive 3-arc-transitive graphs by classifying all such graphs where the automorphism group is an almost simple group with socle an alternating or sporadic group, and all such graphs where…

In this paper, we study the primitive actions of almost simple exceptional groups of Lie type on \(s\)-arc-transitive digraphs. Our motivation is the following question posed by Giudici and Xia: Is there an upper bound on $s$ for finite…

An identifying code of a graph is a subset of its vertices such that every vertex of the graph is uniquely identified by the set of its neighbours within the code. We show a dichotomy for the size of the smallest identifying code in classes…

In this paper we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a non-commutative ring called the skew polynomial rings $F[x;\theta ]$. After a brief description of the skew…