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Long quasi-polycyclic \(t\)-CIS codes. (English) Zbl 1414.94930

Summary: We study complementary information set codes of length \(tn\) and dimension \(n\) of order \(t\) called (\(t\)-CIS code for short). Quasi-cyclic (QC) and quasi-twisted (QT) \(t\)-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 \(1/t\) long QC and QT \(t\)-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 T. P. Berger and N. El Amrani [Finite Fields Appl. 25, 165–181 (2014; Zbl 1305.94107)].

MSC:

94B15 Cyclic codes

Citations:

Zbl 1305.94107

Software:

Magma
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Full Text: DOI arXiv

References:

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