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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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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 establish a new asymptotic expansion of Gurland's ratio of gamma functions, that is, as ,where with and , , are the Bernoulli polynomials. Using a double inequality for hyperbolic functions, we prove that the function is completely monotonic on if , which yields a sharp upper bound for . This shows that the approximation for Gurland's ratio by the truncation of the above asymptotic expansion has a very high accuracy. We also present sharp lower and upper bounds for Gurland's ratio in terms of the partial sum of hypergeometric series. Moreover, some known results are contained in our results when . 相似文献
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We consider four classes of polynomials over the fields , , , , , , , where . We find sufficient conditions on the pairs for which these polynomials permute and we give lower bounds on the number of such pairs. 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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Let χ be an order c multiplicative character of a finite field and a binomial with . We study the twisted classical and T-adic Newton polygons of f. When , we give a lower bound of Newton polygons and show that they coincide if p does not divide a certain integral constant depending on .We conjecture that this condition holds if p is large enough with respect to by combining all known results and the conjecture given by Zhang-Niu. As an example, we show that it holds for . 相似文献
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