A Complete Classification of Ternary Self-Dual Codes of Length 24
Masaaki Harada, Akihiro Munemasa
TL;DR
This paper provides a comprehensive classification of all ternary self-dual codes of length 24, expanding beyond the previously known extremal codes by leveraging the classification of 24-dimensional odd unimodular lattices.
Contribution
It presents the first complete classification of ternary self-dual codes of length 24, including non-extremal codes, using lattice theory.
Findings
Complete list of ternary self-dual codes of length 24
Identification of non-extremal codes
Connection to 24-dimensional odd unimodular lattices
Abstract
Ternary self-dual codes have been classified for lengths up to 20. At length 24, a classification of only extremal self-dual codes is known. In this paper, we give a complete classification of ternary self-dual codes of length 24 using the classification of 24-dimensional odd unimodular lattices.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research