Abstract
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.
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Communicated by P. Wild.
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Harada, M., Munemasa, A. There exists no self-dual [24,12,10] code over \({{\mathbb F}_5}\) . Des. Codes Cryptogr. 52, 125–127 (2009). https://doi.org/10.1007/s10623-009-9271-5
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DOI: https://doi.org/10.1007/s10623-009-9271-5