On the structure of repeated-root polycyclic codes over local rings
Maryam Bajalan, Edgar Martinez-Moro, Reza Sobhani, Steve Szabo and, Gulsum Gozde Yilmazguc
TL;DR
This paper characterizes the structure of repeated-root polycyclic codes over local rings using the Generalized Mattson Solomon polynomial, extending previous single root results and exploring dual code properties.
Contribution
It introduces the Generalized Mattson Solomon polynomial for these codes and details their structural properties and duals over local rings and finite fields.
Findings
Explicit decomposition of codes via idempotents
Structural properties in terms of matrix product codes
Description of dual codes in the polycyclic code class
Abstract
This paper provides the Generalized Mattson Solomon polynomial for repeated-root polycyclic codes over local rings that gives an explicit decomposition of them in terms of idempotents that completes the single root study. It also states some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes. Both approaches provide a description of the -dual code of a given polycyclic code.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · Islamic Finance and Communication