New cyclic relative difference sets constructed from d-homogeneous functions with difference-balanced property
- Authors
- Kim, SH; No, JS; Chung, HB; Helleseth, T
- Issue Date
- Mar-2005
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Keywords
- cyclic difference sets; cyclic relative difference sets; d-homogeneous; functions; p-rank; sequences
- Citation
- IEEE TRANSACTIONS ON INFORMATION THEORY, v.51, no.3, pp.1155 - 1163
- Journal Title
- IEEE TRANSACTIONS ON INFORMATION THEORY
- Volume
- 51
- Number
- 3
- Start Page
- 1155
- End Page
- 1163
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/25209
- DOI
- 10.1109/TIT.2004.842712
- ISSN
- 0018-9448
- Abstract
- For a prime power q, we show that a cyclic relative difference set with parameters (q(n)-1/q-1, q(n-1), q(n-2)) can be constructed from a d-homogeneous function from F, \ fO I onto Fq with difference-balanced property, where F-qn is the finite field with q(n) elements. This construction method enables us to construct several new cyclic relative difference sets with parameters (p(n)-1/p(l)-1, p(l)-1, p(n-l) , p(n-2l)) from p-ary sequences of period p(n)-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.
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