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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.23974 |
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| _version_ | 1866910194889392128 |
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| author | Søreng, Jan |
| author_facet | Søreng, Jan |
| contents | The objective of this work is to establish a mathematical framework for the study of symmetric shift registers over the field GF(2). The present paper gives a new approach where the symmetric shift registers are represented by associated systems of nonlinear difference equations. Arithmetical progressions will play a central part. This approach clarifies the underlying structures and makes it easier to determine the minimal periods of the sequences generated by the symmetric shift registers. Key words: Shift registers, nonlinear difference equations, periods, arithmetical progressions, GF(2).
An open-source implementation of the algorithms presented in this paper is available on GitHub (https://github.com/paalsoreng/symmetric-shift-register). In addition, an interactive web application is provided for experimenting with and evaluating the algorithms in practice (https://paalsoreng.github.io). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation of Symmetric Shift Registers Søreng, Jan Combinatorics Information Theory The objective of this work is to establish a mathematical framework for the study of symmetric shift registers over the field GF(2). The present paper gives a new approach where the symmetric shift registers are represented by associated systems of nonlinear difference equations. Arithmetical progressions will play a central part. This approach clarifies the underlying structures and makes it easier to determine the minimal periods of the sequences generated by the symmetric shift registers. Key words: Shift registers, nonlinear difference equations, periods, arithmetical progressions, GF(2). An open-source implementation of the algorithms presented in this paper is available on GitHub (https://github.com/paalsoreng/symmetric-shift-register). In addition, an interactive web application is provided for experimenting with and evaluating the algorithms in practice (https://paalsoreng.github.io). |
| title | Representation of Symmetric Shift Registers |
| topic | Combinatorics Information Theory |
| url | https://arxiv.org/abs/2505.23974 |