A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR
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-f...
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Belarusian National Technical University
2017-05-01
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| Series: | Системный анализ и прикладная информатика |
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| Online Access: | https://sapi.bntu.by/jour/article/view/152 |
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| author | O. N. Zhdanov A. V. Sokolov |
| author_facet | O. N. Zhdanov A. V. Sokolov |
| author_sort | O. N. Zhdanov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b4aead3f9ca941b5a4982b8a10ba7de2 |
| institution | Kabale University |
| issn | 2309-4923 2414-0481 |
| language | English |
| publishDate | 2017-05-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Системный анализ и прикладная информатика |
| spelling | doaj-art-b4aead3f9ca941b5a4982b8a10ba7de22025-02-03T05:16:50ZengBelarusian National Technical UniversityСистемный анализ и прикладная информатика2309-49232414-04812017-05-0101778510.21122/2309-4923-2017-1-77-85120A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATORO. N. Zhdanov0A. V. Sokolov1Siberian State Aerospace UniversityOdessa National Polytechnic UniversityPractical 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.https://sapi.bntu.by/jour/article/view/152bent-functionsmany-valued logicagievich bent-square |
| spellingShingle | O. N. Zhdanov A. V. Sokolov A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR Системный анализ и прикладная информатика bent-functions many-valued logic agievich bent-square |
| title | A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR |
| title_full | A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR |
| title_fullStr | A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR |
| title_full_unstemmed | A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR |
| title_short | A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR |
| title_sort | synthesis method of basic ternary bent squares based on the triad shift operator |
| topic | bent-functions many-valued logic agievich bent-square |
| url | https://sapi.bntu.by/jour/article/view/152 |
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