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Let M be a random rank-r matrix over the binary field , and let be its Hamming weight, that is, the number of nonzero entries of M.We prove that, as with r fixed and tending to a constant, we have that converges in distribution to a standard normal random variable. 相似文献
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In this paper, we give the dimension and the minimum distance of two subclasses of narrow-sense primitive BCH codes over with designed distance for all , where q is a prime power and is a positive integer. As a consequence, we obtain an affirmative answer to two conjectures proposed by C. Ding in 2015. Furthermore, using the previous part, we extend some results of Yue and Hu [16], and we give the dimension and, in some cases, the Bose distance for a large designed distance in the range for , where if m is odd, and if m is even. 相似文献
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Cyclic code is an interesting topic in coding theory and communication systems. In this paper, we investigate the ternary cyclic codes with parameters based on some results proposed by Ding and Helleseth in 2013. Six new classes of optimal ternary cyclic codes are presented by determining the solutions of certain equations over . 相似文献
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In this paper, based on the structure of embedded fields, we investigate explicit construction of systematic mMDS sliding window codes with memory . First, over GF() with and , we propose an algorithm to construct mMDS codes with memory 2, which are optimal in the sense that is the maximum possible value of k for a sliding window code with memory 2 over GF() to be mMDS. When , every constructed code has the extra property that it contains a mMDS sliding window code with memory 2 as a subcode over the subfield GF(). Next, over GF() with and , we introduce a method to construct mMDS codes memory 3, and a few new codes have been obtained consequently. When , every code constructed by the new approach also has the property that it contains an mMDS subcode over the subfield GF(). The embedding subfield-subcode property enhances the flexibility and efficiency of the designed codes. 相似文献
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《Discrete Mathematics》2023,346(4):113304
In 1965 Erd?s asked, what is the largest size of a family of k-element subsets of an n-element set that does not contain a matching of size ? In this note, we improve upon a recent result of Frankl and resolve this problem for and . 相似文献
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《Discrete Mathematics》2022,345(9):112970
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