Abstract. In this paper, we give some new extremal ternary self-dual codes which are constructed ... more Abstract. In this paper, we give some new extremal ternary self-dual codes which are constructed by skew-Hadamard matrices. This has been achieved with the aid of a recently presented modification of a known con-struction method. In addition, we survey the known results for self-dual ...
In this paper, we demonstrate that the search for weighing matrices constructed from two circulan... more In this paper, we demonstrate that the search for weighing matrices constructed from two circulants can be viewed as a permutation problem. To solve it a set of two competent genetic algorithms (CGAs) are used to locate common integers in two sorted arrays. The motivation to deal with the messy genetic algorithm (mGA) is given from the pioneering results of Goldberg, regarding the ability of the mGA to put tight genes together in a solution which points directly to structural patterns in weighing matrices. In order to take into ...
ABSTRACT Combinatorial designs have been used widely in the construction of self-dual codes. Rece... more ABSTRACT Combinatorial designs have been used widely in the construction of self-dual codes. Recently a new method of constructing self-dual codes was established using orthogonal designs. This method has led to the construction of many new self-dual codes over small finite fields and rings. In this paper, we generalize this method by using generalized orthogonal designs, and we give another new method that creates and solves Diophantine equations over GF(p) in order to find suitable generator matrices for self-dual codes. We show that under the necessary conditions these methods can be applied as well to small and large fields. We apply these two methods to study self-dual codes over GF(31) and GF(37). Using these methods we obtain some new maximum distance separable self-dual codes of small orders.
The average complexity analysis for a formalism pertaining pairs of compatible sequences is prese... more The average complexity analysis for a formalism pertaining pairs of compatible sequences is presented. The analysis is done in two levels, so that an accurate estimate is achieved. The way of separating the candidate pairs into suitable classes of ternary sequences is interesting, allowing the use of fundamental tools of symbolic computation, such as holonomic functions and asymptotic analysis to derive an average complexity of O(n √ n log n) for sequences of length n.
In this paper, we give some methods to generate new secret-sharing schemes from Hadamard matrices... more In this paper, we give some methods to generate new secret-sharing schemes from Hadamard matrices derived through orthogonal 3-designs. A close connection of Hadamard designs and secret-sharing schemes is shown. In addition, we survey some of the most prolific construction methods for Hadamard matrices thus providing the necessary structures to describe a two-part secret-sharing scheme based on Hadamard designs. Furthermore, we exhibit how some algebraic aspects of secret-sharing cryptography are interpreted in ...
Page 1. On-line Appendix to the paper ''New classes of orthogonal designs and w... more Page 1. On-line Appendix to the paper ''New classes of orthogonal designs and weighing matrices derived from near normal sequences'' Christos Koukouvinos and Dimitris E. Simos . In this on-line appendix of the paper we ...
Orthogonal designs (ODs) have numerous applications in Statistics, Telecommunications, Coding The... more Orthogonal designs (ODs) have numerous applications in Statistics, Telecommunications, Coding Theory and Cryptography, see . An OD of order n and type (s 1 , s 2 , . . . , s u ) denoted OD(n; s 1 , s 2 , . . . , s u ) in the commuting variables a 1 , a 2 , . . . , a u , is a square matrix D of order n with entries from the set {0, ±a 1 , ±a 2 , . . . , ±a u } satisfying DD T = u i=1 (s i a 2 i )I n , where I n is the identity matrix of order n. A crucial lemma for manipulating ODs is the following.
Abstract. In this paper, we give some new extremal ternary self-dual codes which are constructed ... more Abstract. In this paper, we give some new extremal ternary self-dual codes which are constructed by skew-Hadamard matrices. This has been achieved with the aid of a recently presented modification of a known con-struction method. In addition, we survey the known results for self-dual ...
In this paper, we demonstrate that the search for weighing matrices constructed from two circulan... more In this paper, we demonstrate that the search for weighing matrices constructed from two circulants can be viewed as a permutation problem. To solve it a set of two competent genetic algorithms (CGAs) are used to locate common integers in two sorted arrays. The motivation to deal with the messy genetic algorithm (mGA) is given from the pioneering results of Goldberg, regarding the ability of the mGA to put tight genes together in a solution which points directly to structural patterns in weighing matrices. In order to take into ...
ABSTRACT Combinatorial designs have been used widely in the construction of self-dual codes. Rece... more ABSTRACT Combinatorial designs have been used widely in the construction of self-dual codes. Recently a new method of constructing self-dual codes was established using orthogonal designs. This method has led to the construction of many new self-dual codes over small finite fields and rings. In this paper, we generalize this method by using generalized orthogonal designs, and we give another new method that creates and solves Diophantine equations over GF(p) in order to find suitable generator matrices for self-dual codes. We show that under the necessary conditions these methods can be applied as well to small and large fields. We apply these two methods to study self-dual codes over GF(31) and GF(37). Using these methods we obtain some new maximum distance separable self-dual codes of small orders.
The average complexity analysis for a formalism pertaining pairs of compatible sequences is prese... more The average complexity analysis for a formalism pertaining pairs of compatible sequences is presented. The analysis is done in two levels, so that an accurate estimate is achieved. The way of separating the candidate pairs into suitable classes of ternary sequences is interesting, allowing the use of fundamental tools of symbolic computation, such as holonomic functions and asymptotic analysis to derive an average complexity of O(n √ n log n) for sequences of length n.
In this paper, we give some methods to generate new secret-sharing schemes from Hadamard matrices... more In this paper, we give some methods to generate new secret-sharing schemes from Hadamard matrices derived through orthogonal 3-designs. A close connection of Hadamard designs and secret-sharing schemes is shown. In addition, we survey some of the most prolific construction methods for Hadamard matrices thus providing the necessary structures to describe a two-part secret-sharing scheme based on Hadamard designs. Furthermore, we exhibit how some algebraic aspects of secret-sharing cryptography are interpreted in ...
Page 1. On-line Appendix to the paper ''New classes of orthogonal designs and w... more Page 1. On-line Appendix to the paper ''New classes of orthogonal designs and weighing matrices derived from near normal sequences'' Christos Koukouvinos and Dimitris E. Simos . In this on-line appendix of the paper we ...
Orthogonal designs (ODs) have numerous applications in Statistics, Telecommunications, Coding The... more Orthogonal designs (ODs) have numerous applications in Statistics, Telecommunications, Coding Theory and Cryptography, see . An OD of order n and type (s 1 , s 2 , . . . , s u ) denoted OD(n; s 1 , s 2 , . . . , s u ) in the commuting variables a 1 , a 2 , . . . , a u , is a square matrix D of order n with entries from the set {0, ±a 1 , ±a 2 , . . . , ±a u } satisfying DD T = u i=1 (s i a 2 i )I n , where I n is the identity matrix of order n. A crucial lemma for manipulating ODs is the following.
Uploads
Papers by Dimitris Simos