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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research
