Almost difference sets and their sequences with optimal autocorrelation

Author

Arasu, K.T. ; Ding, Cunsheng ; Helleseth, Tor ; Kumar, P. Vijay ; Martinsen, Halvard M.

Author_Institution

Dept. of Math. & Stat., Wright State Univ., Dayton, OH, USA

Volume

47

Issue

7

fYear

2001

fDate

11/1/2001 12:00:00 AM

Firstpage

2934

Lastpage

2943

Abstract

Almost difference sets have interesting applications in cryptography and coding theory. We give a well-rounded treatment of known families of almost difference sets, establish relations between some difference sets and some almost difference sets, and determine the numerical multiplier group of some families of almost difference sets. We also construct six new classes of almost difference sets, and four classes of binary sequences of period n≡0 (mod 4) with optimal autocorrelation. We have also obtained two classes of relative difference sets and four classes of divisible difference sets (DDSs). We also point out that a result due to Jungnickel (1982) can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

Keywords

binary sequences; correlation methods; cryptography; optimisation; set theory; almost difference sets; binary sequences; coding theory; cryptography; difference sets; divisible difference sets; numerical multiplier group; optimal autocorrelation; relative difference sets; sequence period; Autocorrelation; Binary sequences; Codes; Computer science; Cryptography; Informatics; Mathematics; Physics; Statistics;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.959271

Filename

959271