Jing YangDepartment of Mathematical Sciences, Tsinghua UniversityMaosheng XiongDepartment of Mathematics, The Hong Kong University of Science andTechnologyLingliXiaBasic Courses Department, Beijing Union University
Finite Fields and Their Applications, 36, 41-62, 2015
Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three nonzeros. Recently, the authors of constructed a class of cyclic codes with arbitrary number of nonzeros, and computed the weight distribution for several cases. In this paper, we determine the weight distribution for a new family of such codes. This is achieved by introducing certain new methods, such as the theory of Jacobi sums over finite fields and subtle treatment of some complicated combinatorial identities.
Andrew L, Stephen Y, Huaiqing Z, et al. A sharp estimate of positive integral points in 6-dimensional polyhedra and a sharp estimate of smooth numbers[J]. Science China-mathematics, 2015, 59(3): 425-444.
Stephen S T Yau · Beihui Yuan · Huaiqing Zuo. On the polynomial sharp upper estimate conjecture in 7-dimensional simplex. 2016.
Yann BUGEAUDI.R.M.A., Universite de Strasbourg et CNRSGuo-Niu HANI.R.M.A., Universite de Strasbourg et CNRSZhi-Ying WENDepartment of Mathematics, Tsinghua UniversityJia-Yan YAODepartment of Mathematics, Tsinghua University
The irrationality exponent of an irrational number $\xi$, which measures the approximation rate of $\xi$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $\xi$. Results obtained so far are rather fragmentary and often treated case by case. In this work, we shall unify all the known results on the subject by showing that the irrationality exponents of large classes of automatic numbers and Mahler numbers (which are transcendental) are exactly equal to $2$. Our classes contain the Thue--Morse--Mahler numbers, the sum of the reciprocals of the Fermat numbers, the regular paperfolding numbers, which have been previously considered respectively by Bugeaud, Coons, and Guo, Wu and Wen, but also new classes such as the Stern numbers and so on. Among other ingredients, our proofs use results on Hankel determinants obtained recently by Han.