Binary and Non-Binary Self-Dual Sequences and Maximum Period Single-Track Gray Codes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912769270349824 |
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| author | Etzion, Tuvi |
| author_facet | Etzion, Tuvi |
| contents | Binary self-dual sequences have been considered and analyzed throughout the years, and they have been used for various applications. Motivated by a construction for single-track Gray codes, we examine the structure and recursive constructions for binary and non-binary self-dual sequences. The feedback shift registers that generate such sequences are discussed. The connections between these sequences and maximum period single-track codes are discussed. Maximum period non-binary single-track Gray codes of length $p^t$ and period $p^{p^t}$ are constructed. These are the first infinite families of maximum period codes presented in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Binary and Non-Binary Self-Dual Sequences and Maximum Period Single-Track Gray Codes Etzion, Tuvi Information Theory Binary self-dual sequences have been considered and analyzed throughout the years, and they have been used for various applications. Motivated by a construction for single-track Gray codes, we examine the structure and recursive constructions for binary and non-binary self-dual sequences. The feedback shift registers that generate such sequences are discussed. The connections between these sequences and maximum period single-track codes are discussed. Maximum period non-binary single-track Gray codes of length $p^t$ and period $p^{p^t}$ are constructed. These are the first infinite families of maximum period codes presented in the literature. |
| title | Binary and Non-Binary Self-Dual Sequences and Maximum Period Single-Track Gray Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2512.09655 |