Improved Constructions of Skew-Tolerant Gray Codes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915016615133184 |
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| author | Himelfarb, Gabriel Sac Schwartz, Moshe |
| author_facet | Himelfarb, Gabriel Sac Schwartz, Moshe |
| contents | We study skew-tolerant Gray codes, which are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an exponential improvement over the known construction. We also provide linear-time encoding and decoding algorithms for our codes. Finally, we extend the definition to non-binary alphabets, and provide constructions of complete $m$-ary skew-tolerant Gray codes for every base $m\geq 3$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_08233 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved Constructions of Skew-Tolerant Gray Codes Himelfarb, Gabriel Sac Schwartz, Moshe Information Theory Discrete Mathematics Combinatorics H.1.1 We study skew-tolerant Gray codes, which are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an exponential improvement over the known construction. We also provide linear-time encoding and decoding algorithms for our codes. Finally, we extend the definition to non-binary alphabets, and provide constructions of complete $m$-ary skew-tolerant Gray codes for every base $m\geq 3$. |
| title | Improved Constructions of Skew-Tolerant Gray Codes |
| topic | Information Theory Discrete Mathematics Combinatorics H.1.1 |
| url | https://arxiv.org/abs/2411.08233 |