[1]杨名慧,文洁晶,冯克勤*.外差组及其通信应用[J].四川师范大学学报(自然科学版),2017,(04):561-568.[doi:10.3969/j.issn.1001-8395.2017.04.021 ]
 YANG Minghui,WEN Jiejing,FENG Keqin.External Difference Families and Their Applications in Communication[J].Journal of SichuanNormal University,2017,(04):561-568.[doi:10.3969/j.issn.1001-8395.2017.04.021 ]
点击复制

外差组及其通信应用()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2017年04期
页码:
561-568
栏目:
特约专稿
出版日期:
2017-04-30

文章信息/Info

Title:
External Difference Families and Their Applications in Communication
文章编号:
1001-8395(2017)04-0561-08
作者:
杨名慧1 文洁晶2 冯克勤3*
1. 中国科学院 信息工程研究所, 北京 100193;
2. 南开大学 陈省身数学研究所, 天津 300071;
3. 清华大学 数学科学系, 北京 100084
Author(s):
YANG Minghui1 WEN Jiejing2 FENG Keqin3
1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100193;
2. Chern Institute of Mathematics, Nankai University, Tianjin 300071;
3. Department of Mathematical Science, Tsinghua University, Beijing 10084
关键词:
差集合 无逗号码 AMD码 认证码 分圆类 分圆数
Keywords:
difference set generalized external difference family(GEDF) AMD code authentication code cyclotomic class cyclotomic number
DOI:
10.3969/j.issn.1001-8395.2017.04.021
摘要:
组合设计在通信中有着广泛的应用.综述近年来基于同步通信,防欺骗数字签名和认证、密秘共享等方面应用背景而提出的一些新型组合设计:外差组以及它的各种推广和变种.解释这些组合设计和通信应用的联系,介绍它们的构作方法和存在性方面的已知结果,以及未解决的问题.
Abstract:
Combinatorial designs have wide applications in communications. This paper is a survey on several new types of combinatorial designs including external difference family and its generalizations and variations, raised recently based on their applications in synchronization communication, authentication, secrete sharing schemes, etc. In this paper we explain the relationship between the new types of combinatorial designs and communication applications, introduce several construction method and existence results of these combinatorial designs and some unsolved problems.

参考文献/References:

[1] 万哲先. 设计理论[M]. 北京:高等教育出版社,2009.
[2] LEVENSHTEIN V I. One method of constructing quasilinear codes providing synchronization in the presence of errors[J]. Prob Inform Transm,1971,7:215-222.
[3] OGATA W, KURSAWA K, STINSON D R, et al. New combinatorial disigns and their applications to authentication codes and secret sharing shemes[J]. Discrete Math,2004,279(1):383-405.
[4] CHANG Y, DING C. Constructions of external difference families and disjoint difference families[J]. Des Codes Cryptogr,2006,40(2):167-185.
[5] CRAMER R, DODIS Y, FEHR S, et al. Detection of algebraic manipulation with applications to robust secret sharing and fuzzy extractors[J]. Lecture Notes in Comput Sci,2008,4965:471-488.
[6] PATERSON M B, STINSON D R. Combinatorial characterizations of algebraic manipulation dectection codes involving generalized difference families[J]. Discrete Math,2016,339(12):2891-2906.
[7] TONCHEV V D. Partitions of differnce sets and code synchronization[J]. Finite Fields and Their Appl,2005,11(3):601-621.
[8] CRAMER R, FEHR S, PADRO C. Algebraic manipulation detection codes[J]. Sci China Math,2013,56(7):1349-1458.
[9] DAVIS J A, HUCZYNSKA S, MULLEN G L. Near-complete external difference families[J]. Des Codes Cryptogr,doi:10.1007/s10623-016-0275-7,2016.
[10] DING C. Optimal and perfect diffence systems of sets[J]. J Combin Theory,2009,A116(1):109-119.
[11] FAN C L, LEI J G, SHAN X L. Constructions of optimal difference systems of sets[J]. Sci China Math,2011,54(1):173-184.
[12] FUJIWARA Y, MOMIHARA K, YAMADA M. Perfect difference systems of sets and Jacobi sums[J]. Discrete Math,2009,309(12):3954-3961.
[13] FUJIWARA Y, TONCHEV V. D. High rate self-synchronizing codes[J]. IEEE Trans Inform Theory,2013,59(4):2328-2335.
[14] HUANG B, WU D. Cyclotomic constructions of external difference families and disjoint difference families[J]. J Combin Des,2009,17(4):334-341.
[15] LEI J, FAN C. Optimal difference systems of sets and partition-type cyclic difference packings[J]. Des Codes Cryptogr,2011,58(2):135-153.
[16] NG S L, PATERSON M B. Disjoint difference families and their applications[J]. Des Codes Cryptogr,2016,78(1):103-127.
[17] STORER T. Cyclotomy and Difference Sets[M]. Chicago:Markham Pub Co,1967.
[18] MUTOH Y, TOCHEV V. Difference systems of sets and cyclotomy[J]. Discrete Math,2008,308(14):2959-2969.
[19] BAO J, JI L, WEI R, et al. New existence and nonexistence results for strong external difference families[J/OL]. arXiv:1612.08385,2016.
[20] HUCZYNSKA S, PATERSON M B. Existence and non-existence results for strong external differenc families[J/OL]. arXiv:1611.05652,2016.
[21] MARTIN W, STINSON D. Some nonexistence results for strong external difference families using character theory[J/OL]. arXiv:1601.06432,2016.
[22] WEN J, YANG M, FENG K. The (n,m,k,λ)-strong external difference family with m≥5 exists[J/OL]. arXiv:1612.09495,2017.
[23] WEN J, YANG M, FENG K. Cyclotomic construction of strong external difference families in finite fields[J/OL]. arXiv:1701.01796,2017.
[24] ARASU K T, JUNGNICKEL D, MA S L, et al. Strong Cayley graphs with λ-μ=-1[J]. J Combin Theory,1994,67(1):116-125.
[25] MA S L. A survey of partial difference sets[J]. Des Codes Cryptogr,1994,4(4):221-261.
[26] LEUNG K H, MA S L. Partial difference sets and Paley parameters[J]. Bull Lond Math Soc,1995,27(6):553-564.
[27] POLHILL J. Paley partial difference sets in groups of order n4 and 9n4 for any odd n > 1[J]. J Cobmin Theory,2010,A117(8):1027-1036.
[28] JEDWAB J, LI S. Construction and nonexistence of strong external difference families[J]. Preprint,2017.

备注/Memo

备注/Memo:
收稿日期:2017-03-02
基金项目:国家自然科学基金(11571007和11471178)
*通信作者简介:冯克勤(1941—),男,教授,主要从事代数、数论和编码密码学理论的研究,E-mail:kfeng@math.tsinghua.edu.cn
更新日期/Last Update: 2017-04-30