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constant composition codes as Subcodes of Cyclic codes

IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第11期57卷 7482-7488页

作者： Luo, Jinquan Helleseth, Tor Yangzhou Univ Sch Math Sci Nanjing 225002 Jiangsu Provinc Peoples R China Univ Bergen Dept Informat Selmer Ctr N-5020 Bergen Norway

constant composition codes are codes where the frequency distribution of the elements in a codeword is the same for all codewords. In this paper, three classes of constant composition codes are constructed. These codes are subcodes of cyclic codes which have few weights occurring among the codewords. The new codes are excellent asymptotically compared to the previously best known constant composition codes.

关键词： constant composition code cyclic code Kasami code quadratic Gauss sum semiprimitive exponential sum

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On constant composition codes

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DISCRETE APPLIED MATHEMATICS 2006年第6期154卷 912-929页

作者： Chu, WS Colbourn, CJ Dukes, P Arizona State Univ Dept Comp Sci & Engn Tempe AZ 85287 USA Univ Victoria Dept Math & Stat Victoria BC V8W 3P4 Canada

A constant composition code over a k-ary alphabet has the property that the numbers of occurrences of the k symbols within a codeword is the same for each codeword. These specialize to constant weight codes in the binary case, and permutation codes in the case that each symbol occurs exactly once. constant composition codes arise in powerline communication and balanced scheduling, and are used in the construction of permutation codes. In this paper, direct and recursive methods are developed for the construction of constant composition codes. (c) 2005 Elsevier B.V. All rights reserved.

关键词： constant composition code constant weight code permutation code

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A new combinatorial approach to the construction of constant composition codes

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Science China Mathematics 2008年第3期51卷 416-426页

作者： YIN JianXing TANG Yu Department of Mathematics Suzhou UniversitySuzhou 215006China

constant composition codes(CCCs)are a new generalization of binary constant weight codes and have attracted recent interest due to their numerous applications. In this paper, a new combinatorial approach to the constr... 详细信息

关键词： constant composition code optimal combinatorial approach construction 05B05 94B25

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Frame difference families and resolvable balanced incomplete block designs

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DESIGNS codeS AND CRYPTOGRAPHY 2018年第12期86卷 2725-2745页

作者： Costa, Simone Feng, Tao Wang, Xiaomiao Univ Brescia Dipartimento DICATAM Via Valotti 9 I-25123 Brescia Italy Beijing Jiaotong Univ Dept Math Beijing 100044 Peoples R China Ningbo Univ Dept Math Ningbo 315211 Zhejiang Peoples R China

Frame difference families, which can be obtained via a careful use of cyclotomic conditions attached to strong difference families, play an important role in direct constructions for resolvable balanced incomplete block designs. We establish asymptotic existences for several classes of frame difference families. As corollaries new infinite families of 1-rotational (pq + 1, p + 1, 1)-RBIBDs over F + p xF + q are derived, and the existence of (125q + 1, 6, 1)-RBIBDs is discussed. We construct (v, 8, 1)-RBIBDs for v. {624, 1576, 2976, 5720, 5776, 10200, 14176, 24480}, whose existence were previously in doubt. As applications, we establish asymptotic existences for an infinite family of optimal constant composition codes and an infinite family of strictly optimal frequency hopping sequences.

关键词： Frame difference family Resolvable balanced incomplete block design Strong difference family Partitioned difference family constant composition code Frequency hopping sequence

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composition Check codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第1期64卷 249-256页

作者： Immink, Kees A. Schouhamer Cai, Kui Turing Machines Inc NL-3016 DK Rotterdam Netherlands Singapore Univ Technol & Design Singapore 487372 Singapore

We present composition check codes for noisy storage and transmission channels with unknown gain and/or offset. In the proposed composition check code, like in systematic error correcting codes, the encoding of the main data into a constant composition code is completely avoided. To the main data, a coded label is appended that carries information regarding the composition vector of the main data. Slepian's optimal detection technique of codewords that are taken from a constant composition code is applied for detection. A first Slepian detector detects the label and subsequently restores the composition vector of the main data. The composition vector, in turn, is used by a second Slepian detector to optimally detect the main data. We compute the redundancy and error performance of the new method, and results of computer simulations are presented.

关键词： constant composition code permutation code flash memory optical recording

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A New Construction of Zero-Difference Balanced Functions and Its Applications

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第8期59卷 5008-5015页

作者： Cai, Han Zeng, Xiangyong Helleseth, Tor Tang, Xiaohu Yang, Yang Hubei Univ Fac Math & Comp Sci Wuhan 430062 Peoples R China Chinese Acad Sci State Key Lab Informat Secur Inst Informat Engn Beijing 100093 Peoples R China Univ Bergen Dept Informat N-5020 Bergen Norway Southwest Jiaotong Univ Prov Key Lab Informat Coding & Transmiss Inst Mobile Commun Chengdu 610031 Peoples R China

In this paper, a new construction of zero-difference balanced functions defined on Z(v) is given, where v is an odd positive integer. Based on the generic constructions proposed by Ding, optimal constant composition codes and perfect difference systems of sets with new parameters can be generated from the zero-difference balanced functions constructed in this paper.

关键词： constant composition code constant weight code difference system of sets generalized cyclotomy zero-difference balanced function

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A new construction of zero-difference balanced functions and two applications

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DESIGNS codeS AND CRYPTOGRAPHY 2019年第10期87卷 2251-2265页

作者： Liu, Junying Jiang, Yupeng Zheng, Qunxiong Lin, Dongdai Chinese Acad Sci State Key Lab Informat Secur Inst Informat Engn Beijing 100093 Peoples R China Univ Chinese Acad Sci Sch Cyber Secur Beijing 100049 Peoples R China State Key Lab Cryptol POB 5159 Beijing 100878 Peoples R China Natl Digital Switching Syst Engn & Technol Res Ct Zhengzhou 450001 Henan Peoples R China

Zero-difference balanced (ZDB) functions are a generalization of perfect nonlinear functions, and have received a lot of attention due to their important applications in coding theory, cryptography, combinatorics and some engineering areas. In this paper, based on cyclotomy and generalized cyclotomy, a construction of a partitioned difference family is presented, and then a class of ZDB functions is obtained. In addition, these ZDB functions are applied to construct optimal constant composition codes and optimal and perfect difference systems of sets.

关键词： Zero-difference balanced function Cyclotomy Generalized cyclotomy constant composition code Difference system of sets

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Minimum Pearson Distance Detection for Multilevel Channels With Gain and/or Offset Mismatch

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第10期60卷 5966-5974页

作者： Immink, Kees A. Schouhamer Weber, Jos H. Turing Machines Inc NL-3016 DK Rotterdam Netherlands Delft Univ Technol Dept Elect Engn Math & Comp Sci NL-2628 CN Delft Netherlands

The performance of certain transmission and storage channels, such as optical data storage and nonvolatile memory (flash), is seriously hampered by the phenomena of unknown offset (drift) or gain. We will show that minimum Pearson distance (MPD) detection, unlike conventional minimum Euclidean distance detection, is immune to offset and/or gain mismatch. MPD detection is used in conjunction with T-constrained codes that consist of q-ary codewords, where in each codeword T reference symbols appear at least once. We will analyze the redundancy of the new q-ary coding technique and compute the error performance of MPD detection in the presence of additive noise. Implementation issues of MPD detection will be discussed, and results of simulations will be given.

关键词： constant composition code permutation code rank modulation flash memory digital optical data storage recording non-volatile memory NVM mismatch adaptive equalisation fading Pearson distance Euclidean distance fading

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Three New Families of Zero-Difference Balanced Functions With Applications

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第4期60卷 2407-2413页

作者： Ding, Cunsheng Wang, Qi Xiong, Maosheng Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Hong Kong Hong Kong Peoples R China Hong Kong Univ Sci & Technol Dept Math Hong Kong Hong Kong Peoples R China

Zero-difference balanced (ZDB) functions integrate a number of subjects in combinatorics and algebra, and have many applications in coding theory, cryptography, and communications engineering. In this paper, three new families of ZDB functions are presented. The first construction gives ZDB functions defined on the abelian groups (GF(q(1)) x, ... , xGF(q(k)),+) with new and flexible parameters. The other two constructions are based on 2-cyclotomic cosets and yield ZDB functions on Z(n) with new parameters. The parameters of optimal constant composition codes, optimal, and perfect difference systems of sets obtained from these new families of ZDB functions are also summarized.

关键词： constant composition code cyclotomic coset difference system of sets generalized cyclotomy zero-difference balanced function

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Optimal FHSs and DSSs via near zero-difference balanced functions

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DISCRETE APPLIED MATHEMATICS 2018年 247卷 433-447页

作者： Xu, Shanding Cao, Xiwang Xu, Guangkui Tang, Chunming Nanjing Univ Aeronaut & Astronaut Dept Math Nanjing 210016 Jiangsu Peoples R China Nanjing Inst Technol Dept Math & Phys Nanjing 211167 Jiangsu Peoples R China Huainan Normal Univ Sch Math Sci Huainan 232001 Peoples R China Guangzhou Univ Guangdong Higher Educ Inst Key Lab Math & Interdisciplinary Sci Guangzhou 510006 Guangdong Peoples R China

Zero-difference balanced (ZDB) functions were introduced by Ding in connection with constructions of optimal constant composition codes and optimal and perfect difference systems of sets. Based on such functions, people have constructed optimal constant weight codes and optimal frequency-hopping sequences. In order to obtain more optimal cryptographic objects, the zero-difference balanced (ZDB) function is generalized to the near zero-difference balanced (N-ZDB) function in the present paper, whose characterizations are partially given. Furthermore, we prove that near zero-difference balanced (N-ZDB) functions are equivalent to partitioned almost difference families (PADFs) in design theory. As the main contribution of this paper, three classes of the N-ZDB functions are proposed by means of the partition of Z(n), where n is an odd positive integer. Employing these N-ZDB functions, we obtain at the same time optimal frequency-hopping sequences and optimal difference systems of sets with flexible parameters. (C) 2018 Elsevier B.V. All rights reserved.

关键词： constant composition code Difference system of sets constant weight code Frequency-hopping sequence Near zero-difference balanced function

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