Asen Bojilov

• PhD
• Professor (Associate) at Sofia University "St. Kliment Ohridski"

In this paper, we address the problem of determining the number of finite field elements with prescribed absolute trace and co-trace for arbitrary characteristic p. We show that this problem can be converted to solving a system of p − 1 linear equations with matrix of coefficients a slight modification of circulant matrix formed by the Kloosterman...

This talk was delivered at the conference dedicated to Prof. Tor Helleseth's 70th birthday.

Let $G$ be a simple $n$-vertex graph and $W\subseteq\V(G)$. We say that $W$ is a $\delta_k$-small set if $$ \sqrt[k]{\frac{\sum_{v\in W}d^k(v)}{\abs W}}\leq n-\abs W. $$ Let $\varphi^{(k)}(G)$ denote the smallest natural number $r$ such that $\V(G)$ decomposes into $r$ $\delta_k$-small sets, and let $\alpha^{(k)}(G)$ denote the maximal number of ve...

Let $G$ be a graph on $n$ vertices. We call a subset $A$ of the vertex set $V(G)$ \emph{$k$-small} if, for every vertex $v \in A$, $\deg(v) \le n - |A| + k$. A subset $B \subseteq V(G)$ is called \emph{$k$-large} if, for every vertex $u \in B$, $\deg(u) \ge |B| - k - 1$. Moreover, we denote by $\varphi_k(G)$ the minimum integer $t$ such that there...

Let $G$ be a simple $n$-vertex graph with degree sequence $d_1,d_2,...,d_n$ and vertex set $\V(G)$. The degree of $v\in\V(G)$ is denoted by $\D(v)$. The smallest integer $r$ for which $\V(G)$ has an $r$-partition $$ \V(G)=V_1\cup V_2\cup...\cup V_r,\quad V_i\cap V_j=\emptyset, \quad,i\neq j $$ such that $\D(v)\leq n-\abs{V_i}$, $\forall v\in V_i$,...

In this paper a general class of linear cyclic codes \(C_{n,q,t}^i , 1\le i\le t\), is defined of length \(n\) and over a field \({ GF}(q)\) with \((n,q)=1\). This class of codes includes as special cases quadratic residue codes, generalized quadratic residue codes, \(e\)-residue codes and \(Q\)-codes. Furthermore, they partially overlap with the f...

Constacyclic codes with one and the same generator polynomial and distinct length are considered. We give a generalization of the previous result of the first author [4] for constacyclic codes. Suitable maps between vector spaces determined by the lengths of the codes are applied. It is proven that the weight distributions of the coset leaders don'...

In this paper we consider a class of cyclic (pm ¡ 1;pm ¡ 2m ¡ 1)-codes overZp, where p 6= 2 is a prime number, and we show that these codes have covering radius at most 3.

The description of the linear cyclic codes as ideals in the algebra F_n= F [x]/(x^n–1), where F is a finite field, is well known in the coding theory. The map cyclic shift is a linear operator in F^n. Our aim is to consider a new method of describing the cyclic codes as invariant subspaces of F^n regarding this operator.

In the coding theory the description of linear cyclic codes in terms of commutative algebra is well known. Since linear codes have the structure of linear subspaces of Fn, the description of linear cyclic codes in terms of linear algebra is natural. We observe that the cyclic shift map is a linear operator in Fn. Our approach is to consider cyclic...

In coding theory the description of linear cyclic codes in terms of commutative algebra is well known. Since linear codes have the structure of linear subspaces of F n , the description of linear cyclic codes in terms of linear algebra is natural. We observe that the cyclic shift map is a linear operator in F n . Our approach is to consider cyclic...