Quasi-Cyclic Complementary Dual Code
Cem G\"uner\.i, Buket \"Ozkaya, Patrick Sol\'e
TL;DR
This paper characterizes quasi-cyclic LCD codes, introduces Hermitian LCD codes, and provides constructions of QCCD codes from larger alphabets, advancing the understanding of LCD code structures and their asymptotic properties.
Contribution
It offers a detailed characterization of quasi-cyclic LCD codes and introduces Hermitian LCD codes, along with new construction methods from larger alphabets.
Findings
Characterization of quasi-cyclic LCD codes
Introduction of Hermitian LCD codes and their cyclic subclass
Construction methods for QCCD codes from larger alphabets
Abstract
LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are introduced to that end and their cyclic subclass is characterized. Constructions of QCCD codes from codes over larger alphabets are given.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Wireless Communication Techniques · graph theory and CDMA systems