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Using Normal Form of Idempotent Matrices over Finite Local Ring Z/p^kZ to Construct Cartesian Authentication Codes 被引量:1
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作者 赵辉芳 南基洙 《Northeastern Mathematical Journal》 CSCD 2007年第2期123-131,共9页
In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probab... In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution. 展开更多
关键词 idempotent matrix finite local ring Cartesian authentication code
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Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings
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作者 Jun Zhang Haiyan Zhou 《Communications in Mathematical Research》 CSCD 2022年第2期206-222,共17页
In this paper, we first propose the maximum arc problem, normal rational curve conjecture, and extensions of normal rational curves over finite local rings, analogously to the finite geometry over finite fields. We th... In this paper, we first propose the maximum arc problem, normal rational curve conjecture, and extensions of normal rational curves over finite local rings, analogously to the finite geometry over finite fields. We then study the deep hole problem of generalized Reed-Solomon (RS) codes over finite local rings. Several different classes of deep holes are constructed. The relationship between finite geometry and deep holes of RS codes over finite local rings are also studied. 展开更多
关键词 finite geometry finite local ring Reed-Solomon code covering radius deep hole
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On Finite Local Rings with Clique Number Four
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作者 Qiong Liu Tongsuo Wu Jin Guo 《Algebra Colloquium》 SCIE CSCD 2022年第1期23-38,共16页
We study the algebraic structure of rings R whose zero-divisor graph T(R)has clique number four.Furthermore,we give complete characterizations of all the finite commutative local rings with clique number 4.
关键词 finite commutative local rings refinements of star graph clique number
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CYCLIC AND NEGACYCLIC CODES OF LENGTH 2p^s OVER F_(p^m) + uF_(p^m) 被引量:2
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作者 刘修生 许小芳 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期829-839,共11页
In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m + uFp^m, where p is an odd prime. On the basis of the works of Dinh (in J.Algebra 324,940-950,2010), we use the Chinese... In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m + uFp^m, where p is an odd prime. On the basis of the works of Dinh (in J.Algebra 324,940-950,2010), we use the Chinese Remainder Theorem to establish the algebraic structure of cyclic and negacyclic codes of length 2p^s over the ring Fp^m + uFp^m in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes. 展开更多
关键词 Negacyclic codes cyclic codes repeated-root codes finite chain ring finite local ring
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On Polynomial Functions over Finite Commutative Rings 被引量:4
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作者 Jian Jun JIANG Guo Hua PENG +1 位作者 Qi SUN Qi Fan ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第4期1047-1050,共4页
Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditi... Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained. 展开更多
关键词 Polynomial function finite commutative local ring Generalized Witt polynomial
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