THE CLASS OF PERFECT TERNARY ARRAYS
In recent decades, perfect algebraic constructions are successfully being use to signal systems synthesis, to construct block and stream cryptographic algorithms, to create pseudo-random sequence generators as well as in many other fields of science and technology. Among perfect algebraic constructi...
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| Format: | Article |
| Language: | English |
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Belarusian National Technical University
2018-08-01
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| Series: | Sistemnyj Analiz i Prikladnaâ Informatika |
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| Online Access: | https://sapi.bntu.by/jour/article/view/213 |
| _version_ | 1797873739747033088 |
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| author | A. V. Sokolov O. N. Zhdanov |
| author_facet | A. V. Sokolov O. N. Zhdanov |
| author_sort | A. V. Sokolov |
| collection | DOAJ |
| description | In recent decades, perfect algebraic constructions are successfully being use to signal systems synthesis, to construct block and stream cryptographic algorithms, to create pseudo-random sequence generators as well as in many other fields of science and technology. Among perfect algebraic constructions a significant place is occupied by bent-sequences and the class of perfect binary arrays associated with them. Bent-sequences are used for development of modern cryptographic primitives, as well as for constructing constant amplitude codes (C-codes) used in code division multiple access technology. In turn, perfect binary arrays are used for constructing correction codes, systems of biphase phase- shifted signals and multi-level cryptographic systems. The development of methods of many-valued logic in modern information and communication systems has attracted the attention of researchers to the improvement of methods for synthesizing many-valued bent-sequences for cryptography and information transmission tasks. The new results obtained in the field of the synthesis of ternary bent-sequences, make actual the problem of researching the class of perfect ternary arrays. In this paper we consider the problem of extending the definition of perfect binary arrays to three-valued logic case, as a result of which the definition of a perfect ternary array was introduced on the basis of the determination of the unbalance of the ternary function. A complete class of perfect ternary arrays of the third order is obtained by a regular method, bypassing the search. Thus, it is established that the class of perfect ternary arrays is a union of four subclasses, in each of which the corresponding methods of reproduction are determined. The paper establishes the relationship between the class of ternary bent-sequences and the class of perfect ternary arrays. The obtained results are the basis for the introduction of perfect ternary arrays into modern cryptographic and telecommunication algorithms. |
| first_indexed | 2024-04-10T01:20:58Z |
| format | Article |
| id | doaj.art-ba4c5f4b1f9b44c9ae38c877c90f8235 |
| institution | Directory Open Access Journal |
| issn | 2309-4923 2414-0481 |
| language | English |
| last_indexed | 2024-04-10T01:20:58Z |
| publishDate | 2018-08-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Sistemnyj Analiz i Prikladnaâ Informatika |
| spelling | doaj.art-ba4c5f4b1f9b44c9ae38c877c90f82352023-03-13T09:47:41ZengBelarusian National Technical UniversitySistemnyj Analiz i Prikladnaâ Informatika2309-49232414-04812018-08-0102475410.21122/2309-4923-2018-2-47-54165THE CLASS OF PERFECT TERNARY ARRAYSA. V. Sokolov0O. N. Zhdanov1Одесский национальный политехнический университетСибирский государственный университет науки и технологий им. академика М. Ф. РешетневаIn recent decades, perfect algebraic constructions are successfully being use to signal systems synthesis, to construct block and stream cryptographic algorithms, to create pseudo-random sequence generators as well as in many other fields of science and technology. Among perfect algebraic constructions a significant place is occupied by bent-sequences and the class of perfect binary arrays associated with them. Bent-sequences are used for development of modern cryptographic primitives, as well as for constructing constant amplitude codes (C-codes) used in code division multiple access technology. In turn, perfect binary arrays are used for constructing correction codes, systems of biphase phase- shifted signals and multi-level cryptographic systems. The development of methods of many-valued logic in modern information and communication systems has attracted the attention of researchers to the improvement of methods for synthesizing many-valued bent-sequences for cryptography and information transmission tasks. The new results obtained in the field of the synthesis of ternary bent-sequences, make actual the problem of researching the class of perfect ternary arrays. In this paper we consider the problem of extending the definition of perfect binary arrays to three-valued logic case, as a result of which the definition of a perfect ternary array was introduced on the basis of the determination of the unbalance of the ternary function. A complete class of perfect ternary arrays of the third order is obtained by a regular method, bypassing the search. Thus, it is established that the class of perfect ternary arrays is a union of four subclasses, in each of which the corresponding methods of reproduction are determined. The paper establishes the relationship between the class of ternary bent-sequences and the class of perfect ternary arrays. The obtained results are the basis for the introduction of perfect ternary arrays into modern cryptographic and telecommunication algorithms.https://sapi.bntu.by/jour/article/view/213многозначная логикасовершенная троичная решеткабент-последовательность |
| spellingShingle | A. V. Sokolov O. N. Zhdanov THE CLASS OF PERFECT TERNARY ARRAYS Sistemnyj Analiz i Prikladnaâ Informatika многозначная логика совершенная троичная решетка бент-последовательность |
| title | THE CLASS OF PERFECT TERNARY ARRAYS |
| title_full | THE CLASS OF PERFECT TERNARY ARRAYS |
| title_fullStr | THE CLASS OF PERFECT TERNARY ARRAYS |
| title_full_unstemmed | THE CLASS OF PERFECT TERNARY ARRAYS |
| title_short | THE CLASS OF PERFECT TERNARY ARRAYS |
| title_sort | class of perfect ternary arrays |
| topic | многозначная логика совершенная троичная решетка бент-последовательность |
| url | https://sapi.bntu.by/jour/article/view/213 |
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