Constructions of almost difference sets from finite fields

Almost difference sets are an interesting subject of combinatorics, and have applications in many areas of engineering such as CDMA communications, error correcting codes and cryptography. The objective of this paper is to present some new constructions of almost difference sets, together with sever...

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Vydáno v:	Designs, codes, and cryptography Ročník 72; číslo 3; s. 581 - 592
Hlavní autoři:	Ding, Cunsheng, Pott, Alexander, Wang, Qi
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Boston Springer US 01.09.2014 Springer
Témata:	Applied sciences Circuits Coding and Information Theory Coding, codes Computer Science Computer science; control theory; systems Computer systems and distributed systems. User interface Cryptography Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Exact sciences and technology Information and Communication Information, signal and communications theory Signal and communications theory Software Telecommunications and information theory 05B10 Partial difference set 51E30 05B30 Skew Hadamard differences set Cyclotomy Difference set Almost difference set 11T22 94C30 Equivalence relation Finite field Code division multiple access Hadamard transformation Error correcting code Cryptography
ISSN:	0925-1022, 1573-7586
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Abstract	Almost difference sets are an interesting subject of combinatorics, and have applications in many areas of engineering such as CDMA communications, error correcting codes and cryptography. The objective of this paper is to present some new constructions of almost difference sets, together with several results on the equivalence relation.
AbstractList	Almost difference sets are an interesting subject of combinatorics, and have applications in many areas of engineering such as CDMA communications, error correcting codes and cryptography. The objective of this paper is to present some new constructions of almost difference sets, together with several results on the equivalence relation.
Author	Ding, Cunsheng Wang, Qi Pott, Alexander
Author_xml	– sequence: 1 givenname: Cunsheng surname: Ding fullname: Ding, Cunsheng organization: Department of Computer Science and Engineering, The Hong Kong University of Science and Technology – sequence: 2 givenname: Alexander surname: Pott fullname: Pott, Alexander organization: Faculty of Mathematics, Institute of Algebra and Geometry, Otto-von-Guericke University Magdeburg – sequence: 3 givenname: Qi surname: Wang fullname: Wang, Qi email: qi.wang@ovgu.de organization: Faculty of Mathematics, Institute of Algebra and Geometry, Otto-von-Guericke University Magdeburg
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Cites_doi	10.1007/s10623-009-9274-2 10.1023/A:1018620002339 10.1006/jabr.2000.8714 10.1007/s10623-008-9216-4
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Keywords	05B10 Partial difference set 51E30 05B30 Skew Hadamard differences set Cyclotomy Difference set Almost difference set 11T22 94C30 Equivalence relation Finite field Code division multiple access Hadamard transformation Error correcting code Cryptography
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References	Feng, Xiang (CR13) 2012; 119 Ding, Wang, Xiang (CR11) 2007; 114 Whiteman (CR22) 1962; 6 Weng, Hu (CR21) 2009; 50 CR4 CR6 Ma (CR14) 1994; 4 Zhang, Lei, Zhang (CR23) 2006; 52 Arasu, Jungnickel, Ma, Pott (CR2) 1994; 67 CR18 CR17 Ding, Helleseth, Lam (CR8) 1999; 45 Ding, Helleseth, Martinsen (CR9) 2001; 47 CR10 Polhill (CR16) 2009; 52 Wang, Du (CR20) 2010; 56 Brouwer, Wilson, Xiang (CR3) 1999; 10 Ding (CR7) 1998; 44 Arasu, Ding, Helleseth, Kumar, Martinsen (CR1) 2001; 47 Davis (CR5) 1992; 59 Ding, Yuan (CR12) 2006; 113 Peisert (CR15) 2001; 240 Tang, Ding (CR19) 2010; 56 9789_CR12 9789_CR23 9789_CR13 9789_CR14 9789_CR15 9789_CR16 9789_CR17 9789_CR18 9789_CR19 9789_CR7 9789_CR8 9789_CR9 9789_CR20 9789_CR10 9789_CR21 9789_CR11 9789_CR22 9789_CR1 9789_CR2 9789_CR3 9789_CR4 9789_CR5 9789_CR6
References_xml	– ident: CR18 – volume: 47 start-page: 428 issue: 1 year: 2001 end-page: 433 ident: CR9 article-title: New families of binary sequences with optimal three-level autocorrelation publication-title: IEEE Trans. Inf. Theory – volume: 56 start-page: 6388 issue: 12 year: 2010 end-page: 6397 ident: CR20 article-title: The linear complexity of binary sequences with optimal autocorrelation publication-title: IEEE Trans. Inf. Theory – ident: CR4 – volume: 240 start-page: 209 issue: 1 year: 2001 end-page: 229 ident: CR15 article-title: All self-complementary symmetric graphs publication-title: J. Algebra – volume: 10 start-page: 25 issue: 1 year: 1999 end-page: 28 ident: CR3 article-title: Cyclotomy and strongly regular graphs publication-title: J. Algebraic Comb. – volume: 113 start-page: 1526 issue: 7 year: 2006 end-page: 1535 ident: CR12 article-title: A family of skew Hadamard difference sets publication-title: J. Comb. Theory Ser. A – ident: CR17 – volume: 56 start-page: 6398 issue: 12 year: 2010 end-page: 6405 ident: CR19 article-title: New classes of balanced quaternary and almost balanced binary sequences with optimal autocorrelation value publication-title: IEEE Trans. Inf. Theory – volume: 4 start-page: 221 issue: 3 year: 1994 end-page: 261 ident: CR14 article-title: A survey of partial difference sets publication-title: Des. Codes Cryptogr. – ident: CR10 – volume: 119 start-page: 245 issue: 1 year: 2012 end-page: 256 ident: CR13 article-title: Cyclotomic constructions of skew Hadamard difference sets publication-title: J. Comb. Theory Ser. A – volume: 67 start-page: 116 issue: 1 year: 1994 end-page: 125 ident: CR2 article-title: Strongly regular Cayley graphs with $$\lambda -\mu =-1$$ publication-title: J. Comb. Theory Ser. A – volume: 59 start-page: 595 issue: 6 year: 1992 end-page: 602 ident: CR5 article-title: Almost difference sets and reversible divisible difference sets publication-title: Arch. Math. (Basel) – ident: CR6 – volume: 44 start-page: 1699 issue: 4 year: 1998 end-page: 1702 ident: CR7 article-title: Autocorrelation values of generalized cyclotomic sequences of order two publication-title: IEEE Trans. Inf. Theory – volume: 50 start-page: 93 issue: 1 year: 2009 end-page: 105 ident: CR21 article-title: Some results on skew Hadamard difference sets publication-title: Des. Codes Cryptogr. – volume: 114 start-page: 867 issue: 5 year: 2007 end-page: 887 ident: CR11 article-title: kew Hadamard difference sets from the Ree-Tits slice symplectic spreads in $$\text{ PG}(3,3^{2h+1})$$ publication-title: J. Comb. Theory Ser. A – volume: 52 start-page: 163 issue: 2 year: 2009 end-page: 169 ident: CR16 article-title: Paley type partial difference sets in non $$p$$ -groups publication-title: Des. Codes Cryptogr. – volume: 47 start-page: 2934 issue: 7 year: 2001 end-page: 2943 ident: CR1 article-title: Almost difference sets and their sequences with optimal autocorrelation publication-title: IEEE Trans. Inf. Theory – volume: 45 start-page: 2606 issue: 7 year: 1999 end-page: 2612 ident: CR8 article-title: Several classes of binary sequences with three-level autocorrelation publication-title: IEEE Trans. Inf. Theory – volume: 6 start-page: 107 year: 1962 end-page: 121 ident: CR22 article-title: A family of difference sets publication-title: Ill J. Math. – volume: 52 start-page: 2052 issue: 5 year: 2006 end-page: 2061 ident: CR23 article-title: A new family of almost difference sets and some necessary conditions publication-title: IEEE Trans. Inf. Theory – ident: 9789_CR16 doi: 10.1007/s10623-009-9274-2 – ident: 9789_CR3 doi: 10.1023/A:1018620002339 – ident: 9789_CR15 doi: 10.1006/jabr.2000.8714 – ident: 9789_CR14 – ident: 9789_CR11 – ident: 9789_CR10 – ident: 9789_CR17 – ident: 9789_CR12 – ident: 9789_CR13 – ident: 9789_CR19 – ident: 9789_CR20 – ident: 9789_CR4 – ident: 9789_CR2 – ident: 9789_CR18 – ident: 9789_CR9 – ident: 9789_CR1 – ident: 9789_CR6 – ident: 9789_CR23 – ident: 9789_CR5 – ident: 9789_CR7 – ident: 9789_CR8 – ident: 9789_CR21 doi: 10.1007/s10623-008-9216-4 – ident: 9789_CR22
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SubjectTerms	Applied sciences Circuits Coding and Information Theory Coding, codes Computer Science Computer science; control theory; systems Computer systems and distributed systems. User interface Cryptography Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Exact sciences and technology Information and Communication Information, signal and communications theory Signal and communications theory Software Telecommunications and information theory
Title	Constructions of almost difference sets from finite fields
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