On the Classification of Type II Codes of Length 24
Noam D. Elkies, Scott D. Kominers
TL;DR
This paper presents a new coding-theoretic proof for classifying Type II codes of length 24, highlighting the analogy between lattices and codes through harmonic weight enumerators.
Contribution
It introduces a novel proof method using harmonic weight enumerators, inspired by lattice theory, to classify Type II codes of length 24.
Findings
New proof of Koch's criterion using harmonic weight enumerators
Strengthens the analogy between lattices and codes in R^{24}
Provides insights into the structure of Type II codes of length 24
Abstract
We give a new, purely coding-theoretic proof of Koch's criterion on the tetrad systems of Type II codes of length 24 using the theory of harmonic weight enumerators. This approach is inspired by Venkov's approach to the classification of the root systems of Type II lattices in R^{24}, and gives a new instance of the analogy between lattices and codes.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications