Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Handbook of Coding Theory
On self-dual codes over $${\mathbb{F}}_5$$
Designs, Codes and Cryptography
Self-dual Codes over Small Prime Fields from Combinatorial Designs
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
Construction of cubic self-dual codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
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Self-dual codes over $${{\mathbb F}_5}$$ exist for all even lengths. The smallest length for which the largest minimum weight among self-dual codes has not been determined is 24, and the largest minimum weight is either 9 or 10. In this note, we show that there exists no self-dual [24, 12, 10] code over $${{\mathbb F}_5}$$ , using the classification of 24-dimensional odd unimodular lattices due to Borcherds.