On Graph-Orthogonal Arrays by Mutually Orthogonal Graph Squares
| Autor: | Ahmed Ibrahim El-Mesady, M. Higazy, Mohamed Mohamed |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics and Astronomy (miscellaneous)
Computer science General Mathematics Cryptography 02 engineering and technology 01 natural sciences orthogonal arrays symbols.namesake Construction method Latin squares: graph squares 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) 0101 mathematics Discrete mathematics business.industry lcsh:Mathematics 010102 general mathematics Graeco-Latin square lcsh:QA1-939 Graph Finite field Chemistry (miscellaneous) Euler's formula symbols 020201 artificial intelligence & image processing Orthogonal array business |
| Zdroj: | Symmetry Volume 12 Issue 11 Symmetry, Vol 12, Iss 1895, p 1895 (2020) |
| ISSN: | 2073-8994 |
| Popis: | During the last two centuries, after the question asked by Euler concerning mutually orthogonal Latin squares (MOLS), essential advances have been made. MOLS are considered as a construction tool for orthogonal arrays. Although Latin squares have numerous helpful properties, for some factual applications these structures are excessively prohibitive. The more general concepts of graph squares and mutually orthogonal graph squares (MOGS) offer more flexibility. MOGS generalize MOLS in an interesting way. As such, the topic is attractive. Orthogonal arrays are essential in statistics and are related to finite fields, geometry, combinatorics and error-correcting codes. Furthermore, they are used in cryptography and computer science. In this paper, our current efforts have concentrated on the definition of the graph-orthogonal arrays and on proving that if there are k MOGS of order n, then there is a graph-orthogonal array, and we denote this array by G-OA(n2,k,n,2). In addition, several new results for the orthogonal arrays obtained from the MOGS are given. Furthermore, we introduce a recursive construction method for constructing the graph-orthogonal arrays. |
| Databáze: | OpenAIRE |
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