For two odd integers m and s with 1≤s < m and gcd(m, s) = 1, let h satisfy h(2~s-1) ≡1(mod 2~m+ 1) and d =(h + 1)(2~m-1) + 1. The cross correlation function between a binary m-sequence of period 22~m-1 and its d-...For two odd integers m and s with 1≤s < m and gcd(m, s) = 1, let h satisfy h(2~s-1) ≡1(mod 2~m+ 1) and d =(h + 1)(2~m-1) + 1. The cross correlation function between a binary m-sequence of period 22~m-1 and its d-decimation sequence is proved to take four values, and the correlation distribution is completely determined. Let n be an even integer and k be an integer with 1≤k≤n/2. For an odd prime p and a p-ary m-sequence {s(t)} of period p^n-1, define u(t) =∑(p^k-1)/2 i=0 s(d_it), where d_i = ip^(n/2) + p^k-i and i = 0, 1,...,(p^k-1)/2. It is proved that the cross correlation function between {u(t)} and {s(t)} is three-valued or four-valued depending on whether k is equal to n/2 or not, and the distribution is also determined.展开更多
Based on a daily precipitation observation dataset of 743 stations in China from 1951 2004, the F distribution function is used to calculate the probability distribution of daily precipitation and to define extreme pr...Based on a daily precipitation observation dataset of 743 stations in China from 1951 2004, the F distribution function is used to calculate the probability distribution of daily precipitation and to define extreme precipitation events. Based on this, the relationship of ENSO and the frequency of extreme precipitation events is studied. Results reveal that ENSO events have impact on extreme precipitation events, with different magnitudes at different regions and seasons. In general, during winter and spring, extreme precipitation events occur more often during E1 Nino events than during La Nina events. While during summer and autumn, the opposite is found. The relationship of a two season-lag ENSO and extreme precipitation frequency shows different pattern. Extreme precipitation events occur more often in several regions if an ENSO warm phase happened in the central-eastern tropical Pacific two seasons before. No similar impacts of El Nino and La Nina on the frequency of extreme precipitation events are found.展开更多
In this paper, the dual code of the binary cyclic code of length 2 n-1 with three zeros α, α t 1 and α t 2 is proven to have five nonzero Hamming weights in the case that n 4 is even and t1 = 2 n/2 + 1, t2 = 2 n-1-...In this paper, the dual code of the binary cyclic code of length 2 n-1 with three zeros α, α t 1 and α t 2 is proven to have five nonzero Hamming weights in the case that n 4 is even and t1 = 2 n/2 + 1, t2 = 2 n-1-2 n/2+1 + 1 or 2 n/2 + 3, where α is a primitive element of the finite field F 2 n . The dual code is a divisible code of level n/2+1, and its weight distribution is also completely determined. When n = 4, the dual code satisfies Ward's bound.展开更多
By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Ni...By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a-1xdto be a complete permutation polynomial over Fp4 k, where d =(p4k-1)/(pk-1)+ 1 and a ∈ F*p4k. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 61170257)
文摘For two odd integers m and s with 1≤s < m and gcd(m, s) = 1, let h satisfy h(2~s-1) ≡1(mod 2~m+ 1) and d =(h + 1)(2~m-1) + 1. The cross correlation function between a binary m-sequence of period 22~m-1 and its d-decimation sequence is proved to take four values, and the correlation distribution is completely determined. Let n be an even integer and k be an integer with 1≤k≤n/2. For an odd prime p and a p-ary m-sequence {s(t)} of period p^n-1, define u(t) =∑(p^k-1)/2 i=0 s(d_it), where d_i = ip^(n/2) + p^k-i and i = 0, 1,...,(p^k-1)/2. It is proved that the cross correlation function between {u(t)} and {s(t)} is three-valued or four-valued depending on whether k is equal to n/2 or not, and the distribution is also determined.
基金supported by the program under Grant No.2007BAC29B04
文摘Based on a daily precipitation observation dataset of 743 stations in China from 1951 2004, the F distribution function is used to calculate the probability distribution of daily precipitation and to define extreme precipitation events. Based on this, the relationship of ENSO and the frequency of extreme precipitation events is studied. Results reveal that ENSO events have impact on extreme precipitation events, with different magnitudes at different regions and seasons. In general, during winter and spring, extreme precipitation events occur more often during E1 Nino events than during La Nina events. While during summer and autumn, the opposite is found. The relationship of a two season-lag ENSO and extreme precipitation frequency shows different pattern. Extreme precipitation events occur more often in several regions if an ENSO warm phase happened in the central-eastern tropical Pacific two seasons before. No similar impacts of El Nino and La Nina on the frequency of extreme precipitation events are found.
基金supported by National Natural Science Foundation of China(Grant Nos. 60973130, 60773134, 10990011)National Basic Research (973) Program of China (Grant No.2007CB311201)supported by Natural Science Foundation for Excellent Youth Scholars of Hubei Province of China (Grant No. 2009CDA147)
文摘In this paper, the dual code of the binary cyclic code of length 2 n-1 with three zeros α, α t 1 and α t 2 is proven to have five nonzero Hamming weights in the case that n 4 is even and t1 = 2 n/2 + 1, t2 = 2 n-1-2 n/2+1 + 1 or 2 n/2 + 3, where α is a primitive element of the finite field F 2 n . The dual code is a divisible code of level n/2+1, and its weight distribution is also completely determined. When n = 4, the dual code satisfies Ward's bound.
基金supported by National Natural Science Foundation of China(Grant Nos.61272481 and 61402352)the China Scholarship Council,Beijing Natural Science Foundation(Grant No.4122089)+1 种基金National Development and Reform Commission(Grant No.20121424)the Norwegian Research Council
文摘By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a-1xdto be a complete permutation polynomial over Fp4 k, where d =(p4k-1)/(pk-1)+ 1 and a ∈ F*p4k. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.
