List Decoding of Quaternary Codes in the Lee Metric
Marcus Greferath, Jens Zumbr\"agel
TL;DR
This paper introduces a list decoding algorithm for quaternary negacyclic codes in the Lee metric, combining algebraic techniques to improve decoding capabilities for these codes.
Contribution
It develops a novel list decoding method for negacyclic codes over b4, integrating Wu's algorithm with Grf6bner basis techniques for the first time.
Findings
Effective decoding of quaternary negacyclic codes in the Lee metric.
Extension of Sudan-Guruswami decoding to ring alphabets.
Enhanced decoding radius for specific code classes.
Abstract
We present a list decoding algorithm for quaternary negacyclic codes over the Lee metric. To achieve this result, we use a Sudan-Guruswami type list decoding algorithm for Reed-Solomon codes over certain ring alphabets. Our decoding strategy for negacyclic codes over the ring combines the list decoding algorithm by Wu with the Gr\"obner basis approach for solving a key equation due to Byrne and Fitzpatrick.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Algebraic structures and combinatorial models