Bounds for Self-Complementary Codes and Their Applications
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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