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On Period of Fibonacci Sequence in Finite Rings with Identity of Order P^2
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作者 Yasemin Tasvurdu Inci Gultekin 《Journal of Mathematics and System Science》 2013年第7期349-352,共4页
In this paper, we obtain the period of generalized Fibonacci sequence in finite rings with identity of order p2 by using equality recursively defined by Fn+2 = A1Fn+1 + A0Fn, for n ≥ 0, where F0 = 0 ( the zero of... In this paper, we obtain the period of generalized Fibonacci sequence in finite rings with identity of order p2 by using equality recursively defined by Fn+2 = A1Fn+1 + A0Fn, for n ≥ 0, where F0 = 0 ( the zero of the ring), F1 = 1 (the identity of the ring) and A0 , A1 are generators elements of finite rings with identity of order p2. Also, we get some results between the period of generalized Fibonacci sequence in the finite rings oforderp2 and characteristic of these rings. 展开更多
关键词 Fibonacci sequence PERIOD finite rings
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Orders of Classical Groups over Finite Rings
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作者 冯红 《Journal of Mathematical Research and Exposition》 CSCD 1998年第4期507-512,共6页
It is observed that a classical group over a finite ring R with identity can be reduced to that over finite fields after the procedures of taking “modulo the radical”, “direct sum” and “tensor products”. B... It is observed that a classical group over a finite ring R with identity can be reduced to that over finite fields after the procedures of taking “modulo the radical”, “direct sum” and “tensor products”. Basing on that fact, we calculate the orders of classical groups over R and the number of k dimensional free submodules of an n dimensional free module over R . 展开更多
关键词 finite ring Nilpotent radical Classifical group Free module.
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Self-Dual Permutation Codes over Finite Chain Rings 被引量:1
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作者 YUAN Yuan ZHANG Huanguo 《Wuhan University Journal of Natural Sciences》 CAS 2007年第6期992-996,共5页
Permutation codes over finite chain rings are introduced; by using the character of the finite chain rings and the knowledge of representation of group, some conditions for existence or non-existence of self-dual perm... Permutation codes over finite chain rings are introduced; by using the character of the finite chain rings and the knowledge of representation of group, some conditions for existence or non-existence of self-dual permutation codes over finite chain rings are obtained. Specially, when the group is a direct product of a 2-group and a T-group, and the group action is transitive, the sufficient and necessary condition of the existence of permutation codes is given. 展开更多
关键词 finite chain ring group code permutation code self-dual code
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Finite Rings Whose Graphs Have Clique Number Less than Five 被引量:1
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作者 Qiong Liu Tongsuo Wu Jin Guo 《Algebra Colloquium》 SCIE CSCD 2021年第3期533-540,共8页
Let R be a commutative ring and Γ(R)be its zero-divisor graph.We completely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one,two,or three.Furthermore,if R■R1&#... Let R be a commutative ring and Γ(R)be its zero-divisor graph.We completely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one,two,or three.Furthermore,if R■R1×R2×…×Rn(each Ri is local for i=1,2,3,...,n),we also give algebraic characterizations of the ring R when the clique number of Γ(R)is four. 展开更多
关键词 finite commutative rings refinements of star graph clique number
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CYCLIC CODES OVER FORMAL POWER SERIES RINGS 被引量:1
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作者 Dougherty Steven T. 刘宏伟 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期331-343,共13页
In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes... In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained. 展开更多
关键词 finite chain rings cyclic codes negacyclic codes γ-adic codes
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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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ON THE CHARACTERIZATION OF CYCLIC CODES OVER TWO CLASSES OF RINGS
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作者 刘修生 《Acta Mathematica Scientia》 SCIE CSCD 2013年第2期413-422,共10页
Let R be a finite chain ring with maximal ideal (7) and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = (C : γ0) C_ (C: 7) C ... C_ (C: γ2) C_ ... Let R be a finite chain ring with maximal ideal (7) and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = (C : γ0) C_ (C: 7) C ... C_ (C: γ2) C_ .-. C_ (C:γ^t-1) can be associated with C, where for any r C R, (C : r) = {e C Rn I re E C}. Using generator elements of the projection of such a tower of codes to the residue field F, we characterize cyclic codes over R. This characterization turns the condition for codes over R to be cyclic into one for codes over the residue field F. Furthermore, we obtain a characterization of cyclic codes over the formal power series ring of a finite chain ring. 展开更多
关键词 finite chain rings formal power series rings cyclic codes tower of codes Hensel lift
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The K_2-groups over Finaite Commutative Rings
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作者 南基洙 田子德 《Northeastern Mathematical Journal》 CSCD 2002年第2期99-102,共4页
The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K... The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups. 展开更多
关键词 K2-group P-GROUP finite commutative ring
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Normal Form of the Elliptic Curve Over the Finite Ring
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作者 Abdelhamid TADMORI Abdelhakim CHILLALI M'hammed ZIANE 《Journal of Mathematics and System Science》 2014年第3期194-196,共3页
In this work, we will to study the equation of an elliptic curve over the ring An = F2d [E], en = 0.,where d. is a positive integer. More precisely we defined the J-invariant of an elliptic curves over the ring An and... In this work, we will to study the equation of an elliptic curve over the ring An = F2d [E], en = 0.,where d. is a positive integer. More precisely we defined the J-invariant of an elliptic curves over the ring An and we establish re(J) = j, wherej is the j-invariant of an elliptic curve over the field F2d and re is the canonical projection defined over ring An by F2d , see [1]. 展开更多
关键词 Elliptic Curves finite ring J-invariant.
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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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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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R_aR_b Transformation of Compound Finite Automata over Commutative Rings 被引量:1
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作者 王浩 《Journal of Computer Science & Technology》 SCIE EI CSCD 1997年第1期40-48,共9页
Some results on RaRb transformation of compound finite automata over finite field are generalized to the case of commutative rings. Properties of RaRb transformation are discussed and applied to the inversion problem ... Some results on RaRb transformation of compound finite automata over finite field are generalized to the case of commutative rings. Properties of RaRb transformation are discussed and applied to the inversion problem for compound finite automata. 展开更多
关键词 finite commutative ring with identity finite automaton compound finite automaton R_aR_b transformation method
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On Nilpotent Finite Alternative Rings with Planar Zero-Divisor Graphs
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作者 A.S. Kuzmina 《Algebra Colloquium》 SCIE CSCD 2016年第4期657-661,共5页
In this paper we prove that any finite nilpotent alternative ring with planar zero-divisor graph is associative.
关键词 zero-divisor graph alternative ring finite ring nilpotent ring planar graph
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Notes on Linear Codes over Finite Commutative Chain Rings
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作者 Zi-hui Liu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第1期141-148,共8页
The properties of the generator matrix are given for linear codes over finite commutative chain rings, and the so-called almost-MDS (AMDS) codes are studied.
关键词 AMDS codes weight hierarchies finite chain rings
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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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MATRIX PRODUCT CODES WITH ROSENBLOOM-TSFASMAN METRIC
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作者 陈博聪 林丽仁 刘宏伟 《Acta Mathematica Scientia》 SCIE CSCD 2013年第3期687-700,共14页
In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obta... In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given. 展开更多
关键词 finite commutative Frobenius ring matrix product code Rosenbloom-Tsfasman metric
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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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Minimal Non—Commutative n—Insertive Rings 被引量:1
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作者 LiQiongXU WeiMinXUE 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第1期141-146,共6页
Let n be an integer with |n| > 1. If p is the smallest prime factor of |n|, we prove that a minimal non-commutative n-insertive ring contains n^4 elements and these rings have five (2p+4) isomorphic classes for p =... Let n be an integer with |n| > 1. If p is the smallest prime factor of |n|, we prove that a minimal non-commutative n-insertive ring contains n^4 elements and these rings have five (2p+4) isomorphic classes for p = 2 (p p 2). 展开更多
关键词 finite rings N insertive rings N commutative rings
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Structure of Abelian rings
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作者 Juncheol HAN Yang LEE Sangwon PARK 《Frontiers of Mathematics in China》 SCIE CSCD 2017年第1期117-134,共18页
Let R be a ring with identity. We use J(R), G(R), and X(R) to denote the Jacobson radical, the group of all units, and the set of all nonzero nonunits in R, respectively. A ring is said to be Abelian if every id... Let R be a ring with identity. We use J(R), G(R), and X(R) to denote the Jacobson radical, the group of all units, and the set of all nonzero nonunits in R, respectively. A ring is said to be Abelian if every idempotent is central. It is shown, for an Abelian ring R and an idempotent-lifting ideal N J(R) of R, that H has a complete set of primitive idempotents if and only if R/N has a complete set of primitive idempotents. The structure of an Abelian ring R is completely determined in relation with the local property when X(R) is a union of 2, 3, 4, and 5 orbits under the left regular action on X(R) by G(R). For a semiperfect ring R which is not local, it is shown that if G(R) is a cyclic group with 2 ∈ G(R), then R is finite. We lastly consider two sorts of conditions for G(R) to be an Abelian group. 展开更多
关键词 Abelian ring regular group action local ring semiperfect ring finite ring Abelian group idempotent-lifting complete set of primitive idempotents
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The maximal size of 6-and 7-arcs in projective Hjelmslev planes over chain rings of order 9 Dedicated to Professor Feng Keqin on the Occasion of his 70th Birthday
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作者 HONOLD Thomas KIERMAIER Michael 《Science China Mathematics》 SCIE 2012年第1期73-92,共20页
We complete the determination of the maximum sizes of (k,n)-arcs, n ≤ 12, in the projective gjelmslev planes over the two (proper) chain rings Z9 = Z/9Z and S3 = F3[X]/(X2) of order 9 by resolving the hitherto ... We complete the determination of the maximum sizes of (k,n)-arcs, n ≤ 12, in the projective gjelmslev planes over the two (proper) chain rings Z9 = Z/9Z and S3 = F3[X]/(X2) of order 9 by resolving the hitherto open cases n = 6 and n = 7. Parts of our proofs rely on decidedly geometric properties of the planes such as Desargues' theorem and the existence of certain subplanes. 展开更多
关键词 Hjelmslev geometry projective Hjelmslev plane arc finite chain ring Galois ring subplane affine subplane
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