Mehmet E. Koroglu

Yildiz Technical University · Department of Mathematics

Linear codes with complementary duals (LCD) have a great deal of significance amongst linear codes. Maximum distance separable (MDS) codes are also an important class of linear codes since they achieve the greatest error correcting and detecting capabilities for fixed length and dimension. The construction of linear codes that are both LCD and MDS...

Constacyclic codes are preferred in engineering applications due to their efficient encoding process via shift registers. The class of constacyclic codes contains cyclic and negacyclic codes. The relation and presentation of cyclic codes as group algebras has been considered. Here for the first time, we establish a relation between constacyclic cod...

In this work, we determine self dual and self orthogonal codes arising from constacyclic codes over group algebras. Also, based on these codes we obtain some good parameters for quantum error-correcting codes.

Construction of good quantum codes via classical codes is an im-portant task for quantum information and quantum computing. In this work,by virtue of a decomposition of the defining set of constacyclic codes we haveconstructed eight new classes of entanglement-assisted quantum maximumdistance separable codes.

The construction of maximum distance separable (MDS) linear complementary dual (LCD) codes and entanglement-assisted quantum MDS (EAQMDS) codes have been of a great interest. In this paper, for arbitrary prime power $q,$ we construct two new families of MDS Hermitian LCD codes of length $n=\frac{{{q^{2}}+1}}{\lambda }$ and $n=\frac{q^{2}-1}{r},$ wh...

Due to their rich algebraic structure, cyclic codes have a great deal of significance amongst linear codes. Duadic codes are the generalization of the quadratic residue codes, a special case of cyclic codes. The $m$-adic residue codes are the generalization of the duadic codes. The aim of this paper is to study the structure of the $m$-adic residue...

In this work, we study the structure of cyclic zero divisor codes over a family of group rings. We determine the number of elements of these codes and introduce the dual codes. Moreover, we show that there is no non-free cyclic LCD $\mathbb{Z}_{4}$ codes.

A linear code with complementary dual (LCD) is a linear code such that ${\cal C} \cap {{\cal C}^ \bot } = \left\{ {\bf{0}} \right\}.$ LCD codes are of great importance due to their wide range of applications in consumer electronics, storage systems and cryptography. Group rings have a rich source of units. Also the well-known structural linear code...

Due to their rich algebraic structure, cyclic codes have a great deal of significance amongst linear codes. Duadic codes are the generalization of the quadratic residue codes, a special case of cyclic codes. The $m$-adic residue codes are the generalization of the duadic codes. The aim of this paper is to study the structure of the $m$-adic residue...

In this work, we study cyclic codes that have generators as Fibonacci polynomials over finite fields. We show that these cyclic codes in most cases produce families of maximum distance separable and optimal codes with interesting properties. We explore these relations and present some examples. Also, we present applications of these codes to secret...

In this paper, we determine self dual and self orthogonal codes arising from negacyclic codes over the group ring (Fq + υFq) G. By taking a suitable Gray image of these codes we obtain many good parameter quantum error-correcting codes over Fq.

In this paper the reversibility problem of a family of two-dimensional cellular automata is completely resolved. It is well known that the reversibility problem is a very difficult one in general. In order to determine whether a cellular automaton is reversible or not the reversibility of its rule matrix is studied via linear algebraic tools. Howev...

Cellular automata-based bit error correcting codes over binary field was originally studied by Chowdhury et al. (IEEE Trans. Comput. 43:759–764, 1994) and also an algorithm for decoding such codes was introduced. Further, for the binary field case, it was shown that cellular automata-based error correcting codes have faster decoding algorithm than...

In this paper, we introduce a family of one dimensional finite linear cellular automata with periodic boundary condition over primitive finite fields with p elements (Zp) which leads to a generalization in two directions: the radius and the field that states take values. This family of cellular automata is called (2r + 1)-cyclic cellular automata s...

The reversibility problem for linear cellular automata with null boundary defined by a rule matrix in the form of a pentadiagonal matrix was studied over the binary field ℤ2 by Martín del Rey et al. [Appl. Math. Comput.217, 8360 (2011)]. Recently, the reversibility problem of 1D Cellular automata with periodic boundary has been extended to ternary...

Cellular automata are simple mathematical representation of complex dynamical systems. Therefore there are several applications of cellular automata in many areas such as coding, cryptography, VLSI design etc. [1, 2]. In this study, a recurrence relation for computation minimal polynomial of rule matrix of linear elementary rule 150 with reflectiv...

Reed-Solomon codes are very convenient for burst error correction which occurs frequently in applications, but as the number of errors increase, the circuit structure of implementing Reed-Solomon codes becomes very complex. An alternative solution to this problem is the modular and regular structure of cellular automata which can be constructed wit...

We propose and test two dimensional linear hybrid cellular automata with Moore neighborhood instead of linear Wolfram cellular automata to determine whether it is convenient to using as a pseudo random number generator. The preliminary results show significance of generating pseudorandom numbers. These hybrid cellular automata have passed the well-...

In this work we introduce and study a new family of one dimensional nonlinear cellular automaton which we name as quadratic cellular automata over ternary fields ( 3 Z ). This family is defined by using the quadratic forms as local transition functions. Further, we define hybrid quadratic cellular automata. Under periodic, null, and reflective boun...