Circulant matrix representation of PN-sequences with ideal autocorrelation property

Abstract

In this paper, we investigate PN-sequences with ideal autocorrelation property and the consequences of this property on the number of +1s and -1s and run structure of sequences. We begin by discussing and surveying about the length of PN-sequences with ideal autocorrelation property. From our discussion and survey we introduce circulant matrix representation of PN-sequence. Through circulant matrix representation we obtain system of non-linear equations that lead to ideal autocorrelation property. Rewriting PN-sequence and its autocorrelation property in {0,1} leads to a definition based on Hamming weight and Hamming distance and hence we can easily prove some results on the PN-sequences with ideal autocorrelation property.