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Let M be a random m×n rank-r matrix over the binary field F2, and let wt(M) be its Hamming weight, that is, the number of nonzero entries of M.We prove that, as m,n+ with r fixed and m/n tending to a constant, we have thatwt(M)12r2mn2r(12r)4(m+n)mn converges in distribution to a standard normal random variable.  相似文献   

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《Discrete Mathematics》2022,345(10):113000
Let F2n be a finite field with 2n elements and fc_(x)=c0x2m(2k+1)+c1x2m+k+1+c2x2m+2k+c3x2k+1F2n[x], where n, m and k are positive integers with n=2m and gcd?(m,k)=e. In this paper, motivated by a recent work of Li, Xiong and Zeng (Li et al. (2021) [12]), we further study the boomerang uniformity of fc_(x) by using similar ideas and carrying out particular techniques in solving equations over finite fields. As a consequence, we generalize Li, Xiong and Zeng's result from the case of m being odd and e=1 to that of both m/e and k/e being odd.  相似文献   

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We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator ?h2Δ+V(|x|)?E in dimension n2, where h,E>0, and V:[0,)R is L and compactly supported. The weighted resolvent norm grows no faster than exp?(Ch?1), while an exterior weighted norm grows h?1. We introduce a new method based on the Mellin transform to handle the two-dimensional case.  相似文献   

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