Abstract: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 also 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.
From: Tuvi Etzion [view email]
[v1]
Wed, 10 Dec 2025 13:50:54 UTC (102 KB)
[v2]
Tue, 16 Dec 2025 18:39:17 UTC (101 KB)
[v3]
Mon, 29 Jun 2026 14:09:05 UTC (101 KB)
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