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New Cyclic Relative Difference Sets Constructed From d-Homogeneous Functions With Difference-Balanced Property.
- Source :
-
IEEE Transactions on Information Theory . Mar2005, Vol. 51 Issue 3, p1155-1163. 9p. - Publication Year :
- 2005
-
Abstract
- For a prime power q, we show that a cyclic relative difference set with parameters (qn-1/q-1, q-1, qn-2) can be constructed from a d-homogeneous function from Fqn / {0} onto Fq with difference-balanced property, where Fqn is the finite field with qn elements. This construction method enables us to construct several new cyclic relative difference sets with parameters (pn-1/pl-1, pl - 1, pn-1, pn-2t) from p-ary sequences of period pn- 1 with ideal autocorrelation property introduced by Helleseth and Gong. Using a lifting idea, other new cyclic relative difference sets can be constructed from the Helleseth-Gong (HG) sequences. Also, the 3-ranks and the trace representation of the characteristic sequences of cyclic relative difference sets from a specific class of ternary HG sequences and ternary Lin sequences are derived. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 51
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 16348763
- Full Text :
- https://doi.org/10.1109/TIT.2004.842712