Hamming Space Levenshtein Bounds Potential Functions Energy of a Code Error-correcting Codes τ-Designs Signed Measures
Issue Date:
2022
Publisher:
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation:
Mathematics and Education in Mathematics, 2022, 100p-112p
Abstract:
We survey recent results on universal bounds on the energy of codes in Hamming
spaces. The universality means, in particular, that the bounds hold for a large class of potential functions (the most important bounds – for absolutely monotone interactions). Furthermore, we employ signed measures that are positive definite up to
certain degrees to establish Levenshtein-type upper bounds on the cardinality of codes
with given minimum and maximum distance, and universal lower bounds on the potential energy for codes with given maximum distance and cardinality. In particular,
the results extend the Levenshtein framework. 2020 Mathematics Subject Classification: 74G65, 94B65, 52A40, 05B30.
