Browse > Article
http://dx.doi.org/10.13089/JKIISC.2002.12.2.11

New Cyclic Relative Difference Sets Constructed from d-Homogeneous Functions with Difference-balanced Property  

김상효 (서울대학교 전기·컴퓨터공학부)
노종선 (서울대학교 전기·컴퓨터공학부)
Publication Information
Journal of the Korea Institute of Information Security & Cryptology / v.12, no.2, 2002 , pp. 11-20 More about this Journal
Abstract
In this paper, for many prime power q, it is shown that new cyclic relative difference sets with parameters (equation omitted) can be constructed by using d-homogeneous functions on $F_{q^{n}}${0} over $F_{q}$ with difference-balanced property, where $F_{q^{n} }$ is a finite field with $q^{n}$ elements. Several new cyclic relative difference sets with parameters (equation omitted) are constructed by using p-ary sequences of period $q^{n}$ -1 with ideal autocorrelation property introduced by Helleseth and Gong and d-form sequences.
Keywords
Difference sets; Cyclic difference sets; Relative difference sets; d-homogeneous functions;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Finite Fields /
[ R. Lidl;H. Niederreiter ] / Encyclopedia of mathematics and Its Applications
2 Cyclic relative difference sets and their p-ranks /
[ D. Chandler;Q. Xiang ] / preprint
3 p-ary unified sequences: p-ary extended d-form sequences with ideal autocorrelation properties /
[ J.S. No ] / preprint
4 A theorem in finite projective geometry and some applications to number theory /
[ J. Singer ] / Trans. Amer. Math. Soc.   DOI   ScienceOn
5 Difference sets: and introduction /
[ D. Jungnickel;A. Pott;A. Pott(ed.);P.V. Kumar(ed.);T. Helleseth(ed.);D. Jungnickel(ed.) ] / Difference Sets, Sequences and their Corr- elation Properties
6 Cyclic Difference Sets /
[ L.D. Baumert ] / Lecture Notes in Mathematics
7 Difference sets /
[ D. Jungnickel;J. Dinitz(ed.);D.R. Stinson(ed.) ] / Contemporary design Theory: A Coll- ection for Surveys
8 A new family of ternary sequences with ideal two-level autocorrelation /
[ T. Helleseth;P.V. Kumar;H.M. Martinsen ] / preprint
9 Some new difference sets /
[ B. Gordon;W.H. Mills;L.R. Welch ] / Canad. J. Math.   DOI
10 Cyclic difference sets with Singer parameters /
[ J.F. Dillon;H. Dobbertin ] / preprint
11 /
[ T. Beth;d. Jungnickel;H. Lenz ] / Design Theory(Second edition)
12 Gauss sums, jacobi sums and p-ranks of cyclic difference sets /
[ R. Evans;H. Hollman;C. Krattenthaler;Q. Xiang ] / preprint
13 New cyclic difference sets with Singer parameters constructed from d-homogeneous function /
[ J.S. No ] / preprint
14 d-form sequence: Families of sequences with low correlation values and large linear spans /
[ A. Klapper ] / IEEE Trans. Inform. Theory   DOI   ScienceOn
15 New nonbinary sequences with ideal two-level autocorrelation function /
[ T. Helleseth;g. Gong ] / preprint