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cyclic codes OVER FORMAL POWER SERIES RINGS

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Acta Mathematica Scientia 2011年第1期31卷 331-343页

作者： Dougherty Steven T. 刘宏伟 Department of Mathematics University of Scranton Department of Mathematics Huazhong Normal University

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.

关键词： Finite chain rings cyclic codes negacyclic codes γ-adic codes

On cyclic codes with Length 2pe over Finite Fields

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Chinese Journal of Electronics 2020年第4期29卷 672-677页

作者： PANG Binbin ZHU Shixin SUN Zhonghua School of Mathematics Hefei University of Technology

cyclic codes are an important class of linear *** codes are applied in data storage,communication systems and consumer electronics due to their efficient encoding and decoding *** utilize the cyclotomy of order 2 to study the cyclic codes with length n = 2peand dimension k = n/2 = *** cyclic codes from our construction are either optimal or almost optimal among all cyclic codes with the same length and *** get the enumeration of these cyclic codes and study the hull of cyclic codes of length n over *** obtain the range of ? = dim(Hull（C）).Finally, we construct and enumerate cyclic codes of length n having hull of given dimension.

关键词： cyclic codes Cyclotomy Hull Primitive root

The Weight Distribution of a Class of p-Ary cyclic codes with Few Weights

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Chinese Journal of Electronics 2020年第4期29卷 717-723页

作者： LIU Li XIE Xianhong School of Mathematics Hefei University of Technology Key Laboratory of Electromagnetic Space Information CAS University of Science and Technology of China

In this paper, we investigate a class of p-ary cyclic codes whose duals have two zeros for some special cases and calculate their weight distributions *** results show that the codes have at most five nonzero ***, the... 详细信息

关键词： cyclic codes Weight distributions Fourier expansion Gauss sums Griesmer bound

cyclic AND NEGAcyclic codes OF LENGTH 2p^s OVER F_(p^m) + uF_(p^m)

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Acta Mathematica Scientia 2014年第3期34卷 829-839页

作者：刘修生许小芳 School of Mathematics and Physics Hubei Polytechnic University

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 *** 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.

关键词： Negacyclic codes cyclic codes repeated-root codes finite chain ring finite local ring

Quaternion Integers Based Higher Length cyclic codes and Their Decoding Algorithm

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Computers, Materials & Continua 2022年第10期73卷 1177-1194页

作者： Muhammad Sajjad Tariq Shah Mohammad Mazyad Hazzazi Adel R.Alharbi Iqtadar Hussain Department of Mathematics Quaid-I-Azam UniversityIslamabad45320Pakistan Department of Mathematics College of ScienceKing Khalid UniversityAbha61413Saudi Arabia College of Computing and Information Technology University of TabukTabuk71491Saudi Arabia Department of Mathematics Statistics and PhysicsQatar UniversityDoha2713Qatar

The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number *** these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have *** continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction *** this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of ***,the error correction capability and code rate tradeoff of these codes are also ***,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.

关键词： Mannheim distance monoid ring cyclic codes parity check matrix extension syndromes decoding code rate and error correction capability

ON THE CHARACTERIZATION OF cyclic codes OVER TWO CLASSES OF RINGS

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Acta Mathematica Scientia 2013年第2期33卷 413-422页

作者：刘修生 School of Mathematics and Physics Hubei Polytechnic University

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.

关键词： Finite chain rings formal power series rings cyclic codes tower of codes Hensel lift

Chinese product of constacyclic and cyclic codes over finite rings

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The Journal of China Universities of Posts and Telecommunications 2013年第3期20卷 109-113页

作者： TANG Yong-sheng ZHU Shi-xin School of Mathematics Hefei University of Technology Department of Mathematics Hefei Normal University

In this paper, we study the Gray images of the Chinese product of constacyclic and cyclic codes over a finite ring. We first introduce the Chinese product of constacyclic and cyclic codes over the finite ring. We then define a Gray map between codes over the finite ring and a finite field. We prove that the Gray image of the Chinese product of constacyclic codes over the finite ring is a distance-invariant quasi-cyclic code over the finite field. We also prove that each code over the finite field, which is the Gray image of the Chinese product of cyclic codes over the finite ring, is permutation equivalent to a quasi-cyclic code.

关键词： Chinese remainder theorem constacyclic codes cyclic codes quasi-cyclic codes

Linear recurring sequences and subfield subcodes of cyclic codes

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Science China Mathematics 2013年第7期56卷 1413-1420页

作者： GAO ZhiHan FU FangWei Department of Combinatorics and Optimization University of Waterloo Chern Institute of Mathematics and LPMC Nankai University

Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm . Denote the restriction of Mqm(f(x)) to sequences over Fq and the set after applying trace function to each sequence in Mqm(f(x)) by Mqm(f(x)) | Fq and Tr( Mqm(f(x))), respectively. It is shown that these two sets are both complete sets of linear recurring sequences over Fq with some characteristic polynomials over Fq. In this paper, we firstly determine the characteristic polynomials for these two sets. Then, using these results, we determine the generator polynomials of subfield subcodes and trace codes of cyclic codes over Fqm .

关键词： linear recurring sequences characteristic polynomial cyclic codes subfield subcodes trace codes

PERIOD DISTRIBUTION OF cyclic codes OVER F_q + uF_q +···+u^(m-1)F_q

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Journal of Electronics(China) 2014年第6期31卷 547-551页

作者： Li Ping Zhong Jiawei Zhu Shixin School of Mathematics Hefei University of Technology

In this paper, the period distribution of cyclic codes overR = F_q + uF_q +···+u^(m-1)F_q is studied, where um= 0 and q is a prime power. A necessary and sufficient condition for the existence of period of cyclic codes over R is given. The period distributions of cyclic codes over R and their dual codes are determined by employing generator polynomial. The counting formulas of the period distributions of cyclic codes over R and their dual codes are obtained.

关键词： cyclic codes Dual codes Period Period distribution