Classification and count of binary linear complementary dual group codes
Ankan Shaw, Sanjit Bhowmick, Satya Bagchi
TL;DR
This paper provides a comprehensive classification of binary group codes with complementary duals, detailing their structure, enumeration, and properties, including connections to MDS codes and maximal ideals.
Contribution
It offers a complete classification of binary LCD group codes and explicitly determines their number using cyclotomic cosets, also exploring their dimensions and minimum distances.
Findings
Explicit enumeration of LCD cyclic group codes.
Established connections between LCD MDS group codes and maximal ideals.
Analyzed dimensions and minimum distances of LCD group codes.
Abstract
We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and the minimum distance for LCD group codes are explored. Finally, we find a connection between LCD MDS group codes and maximal ideals.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding