Bounds for Self-Complementary Codes and Their Applications
Bounds for Self-Complementary Codes and Their Applications
复制标题
自补码的界限及其应用
DOI：
10.1007/978-3-7091-2786-5_14
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
V. Levenshtein
中科院分区：
文献类型：
--
作者：
V. Levenshtein
考虑汉明空间中的自补码，即与任何向量一起包含其补码的二进制码。文中给出的最小距离给定的自补码码的大小的界一般好于Hamming空间中任意二进制码的相应的界。给出了这个界在估计自对偶二进制码的最小距离、任意二进制码的互相关性、多项式的勒让德符号和的模以及二进制码的一些随机性参数等方面的一些应用。
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 distancedpresented 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.