The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely ma...The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely many roots. Then the properties of quaternion algebra over Zp are discussed,and the order of its unit group is determined. Lastly,another ring isomorphism of M2（Zp） and the quaternion algebra over Zp when p satisfies some particular conditions are presented.展开更多
The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k sym...The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.展开更多
文摘The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely many roots. Then the properties of quaternion algebra over Zp are discussed,and the order of its unit group is determined. Lastly,another ring isomorphism of M2（Zp） and the quaternion algebra over Zp when p satisfies some particular conditions are presented.
基金supported by the National Natural Science Foundation of China under Grant No. 61063041the Program for New Century Excellent Talents of Universities in Fujian Province under Grant No. JK2010047the Funds of the Education Department of Gansu Province under Grant No. 1001-09
文摘The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.
