Abstract
Self-complementary codes in the Hamming space, i.e., binary codes that together with any vector contain its complement, are considered. The bound on the size of a self-complementary code with a given minimum distance d presented here is in general better than the corresponding bound for arbitrary binary codes in the Hamming space. Some applications of this bound for estimating the minimum distance of self-dual binary codes, the cross-correlation of arbitrary binary codes, the modulus of sums of Legendre symbols of polynomials, and some parameters of randomness properties of binary codes, are given.
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© 1993 Springer-Verlag Wien
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Levenshtein, V.I. (1993). Bounds for Self-Complementary Codes and Their Applications. In: Camion, P., Charpin, P., Harari, S. (eds) Eurocode ’92. International Centre for Mechanical Sciences, vol 339. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2786-5_14
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DOI: https://doi.org/10.1007/978-3-7091-2786-5_14
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82519-8
Online ISBN: 978-3-7091-2786-5
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