On the burst-covering radius of binary cyclic codes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910109904404480 |
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| author | Himelfarb, Gabriel Sac Schwartz, Moshe |
| author_facet | Himelfarb, Gabriel Sac Schwartz, Moshe |
| contents | We define and study burst-covering codes. We provide some general bounds connecting the parameters of a code with its burst-covering radius. We then provide stronger bounds on the burst-covering radius of cyclic codes, by employing linear-feedback shift-register (LFSR) sequences. For the case of BCH codes we prove a new bound on pattern frequencies in LFSR sequences, which is of independent interest. Using this tool, we can bound the burst-covering radius of binary primitive BCH codes and Melas codes. We then present an efficient burst-covering algorithm for cyclic codes. Finally, we present a bound on the critical exponent of cyclic codes based on the burst-covering radius. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00435 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the burst-covering radius of binary cyclic codes Himelfarb, Gabriel Sac Schwartz, Moshe Information Theory 94B15, 94B20, 94A55 We define and study burst-covering codes. We provide some general bounds connecting the parameters of a code with its burst-covering radius. We then provide stronger bounds on the burst-covering radius of cyclic codes, by employing linear-feedback shift-register (LFSR) sequences. For the case of BCH codes we prove a new bound on pattern frequencies in LFSR sequences, which is of independent interest. Using this tool, we can bound the burst-covering radius of binary primitive BCH codes and Melas codes. We then present an efficient burst-covering algorithm for cyclic codes. Finally, we present a bound on the critical exponent of cyclic codes based on the burst-covering radius. |
| title | On the burst-covering radius of binary cyclic codes |
| topic | Information Theory 94B15, 94B20, 94A55 |
| url | https://arxiv.org/abs/2601.00435 |