A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR
https://doi.org/10.21122/2309-4923-2017-1-77-85
Abstract
Practical application of advanced algebraic constructions in modern communication systems based on MC-CDMA (Multi Code Code Division Multiple Access) technology and in cryptography necessitates their further research. One of the most commonly used advanced algebraic construction is the binary bent-function having a uniform amplitude spectrum of the Walsh-Hadamard transform and, accordingly, having the maximal distance from the codewords of affine code. In addition to the binary bent-functions researchers are currently focuses on the development of synthesis methods of their many-valued analogues. In particular, one of the most effective methods for the synthesis of many-valued bent-functions is the method based on the Agievich bent-squares. In this paper, we developed a regular synthesis method of the ternary bent-squares on the basis of an arbitrary spectral vector and the regular operator of the triad shift. The classification of spectral vectors of lengths N = 3 and N = 9 is performed. On the basis of spectral classification more precise definition of many-valued bent-sequences is given, taking into account the existence of the phenomenon of many-valued bent-sequences for the length, determined by odd power of base. The paper results are valuable for practical use: the development of new constant amplitude codes for MC-CDMA technology, cryptographic primitives, data compression algorithms, signal structures, algorithms of block and stream encryption, based on advanced principles of many-valued logic. The developed bent-squares design method is also a basis for further theoretical research: development of methods of the permutation of rows and columns of basic bent-squares and their sign coding, synthesis of composite bent-squares. In addition, the data on the spectral classification of vectors give the task of constructing the synthesis methods of bent-functions of lengths N = 32k+1, k Є ℕ.
About the Authors
O. N. Zhdanov
Siberian State Aerospace University
Russian Federation
Russian Federation
Zhdanov Oleg Nikolaevich - Ph. D., Associate Professor of Informational Technologies department
A. V. Sokolov
Odessa National Polytechnic University
Ukraine
Ukraine
Artem V. Sokolov - Ph. D. , senior lecturer of the Data Security department
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Review
For citations:
Zhdanov O.N., Sokolov A.V. A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR. «System analysis and applied information science». 2017;(1):77-85. (In Russ.) https://doi.org/10.21122/2309-4923-2017-1-77-85
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