Long quasi-polycyclic $t-$ CIS codes

Adel Alahmadi; Cem Güneri; Hatoon Shoaib; Patrick Solé

doi:10.3934/amc.2018013

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2018, Volume 12, Issue 1: 189-198. Doi: 10.3934/amc.2018013

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Long quasi-polycyclic $t-$ CIS codes

1.
Math. Dept., King Abdulaziz University, Jeddah, Saudi Arabia
2.
Sabancı University, FENS, 34956 Istanbul, Turkey
3.
Université de Paris 8, 2 rue de la Liberté, 93 526 Saint-Denis, France

Received: January 31, 2017

Published: February 2018

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Abstract

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 Berger and Amrani.

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Mathematics Subject Classification: 94B60, 12E20.

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