[Yan, Tongjiang] China Univ Petr, Coll Math & Computat Sci, Dongying 257061, Peoples R China. [Yan, Tongjiang] Chinese Acad Sci, Inst Software, State Key Lab Informat Secur, Beijing 100190, Peoples R China. [Xiao, Guozhen] Xidian Univ, ISN Natl Key Lab, Xian 710071, Peoples R China.
Abstract:
In this correspondence, we consider the equivalent condition that a sequence possesses ideal autocorrelation function. As we know, for a binary sequence, the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets. This paper proves that, for a p-ary sequence with d-form property, the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p - 1 relative difference sets. Moreover, a new way to construct cyclic divisible difference sets is presented. (C) 2013 Elsevier Inc. All rights reserved.
English Abstract:
In this correspondence, we consider the equivalent condition that a sequence possesses ideal autocorrelation function. As we know, for a binary sequence, the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets. This paper proves that, for a p-ary sequence with d-form property, the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p - 1 relative difference sets. Moreover, a new way to construct cyclic divisible difference sets is presented. (C) 2013 Elsevier Inc. All rights reserved.