On the classification of completely regular codes with covering radius two and antipodal dual
J. Borges, D. V. Zinoviev, V. A. Zinoviev
TL;DR
This paper classifies a specific class of linear completely regular codes with covering radius two, focusing on their duals being antipodal, and explores properties of their dual two-weight codes.
Contribution
It provides a complete classification of these codes and analyzes the properties of their dual two-weight codes, which was previously unexplored.
Findings
All such codes are classified explicitly.
Dual codes are shown to be two-weight codes.
Properties of these dual codes are characterized.
Abstract
We classify all linear completely regular codes which have covering radius and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · graph theory and CDMA systems