Long quasi-polycyclic \begin{document}$t-$\end{document} CIS codes
| Autor: | Hatoon Shoaib, Adel Alahmadi, Cem Güneri, Patrick Solé |
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| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
Code (set theory) Algebra and Number Theory Conjecture Computer Networks and Communications Applied Mathematics Dimension (graph theory) Structure (category theory) Order (ring theory) 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Microbiology Combinatorics 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Tornado code Primitive root modulo n Mathematics |
| Zdroj: | Advances in Mathematics of Communications. 12:189-198 |
| ISSN: | 1930-5338 |
| DOI: | 10.3934/amc.2018013 |
| Popis: | We study complementary information set codes of length \begin{document}$tn$\end{document} and dimension \begin{document}$n$\end{document} of order \begin{document}$t$\end{document} called ( \begin{document}$t-$\end{document} CIS code for short). Quasi-cyclic (QC) and quasi-twisted (QT) \begin{document}$t$\end{document} -CIS codes are enumerated by using their concatenated structure. Asymptotic existence results are derived for one-generator and fixed co-index QC and QT codes depending on Artin's primitive root conjecture. This shows that there are infinite families of rate \begin{document}$1/t$\end{document} long QC and QT \begin{document}$t$\end{document} -CIS codes with relative distance satisfying a modified Varshamov-Gilbert bound. Similar results are defined for the new and more general class of quasi-polycyclic codes introduced recently by Berger and Amrani. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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