Cross-Correlation between a p-Ary m-Sequence and Its All Decimated Sequences for $d= rac{(p^{m}+1)(p^{m}+p-1)}{p+1}$

Yongbo XIA  Shaoping CHEN  Tor HELLESETH  Chunlei LI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.4   pp.964-969
Publication Date: 2014/04/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.964
Type of Manuscript: PAPER
Category: Information Theory
Keyword: 
p-ary m-sequence,  decimated sequence,  correlation function,  quadratic form,  

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Summary: 
Let m ≥ 3 be an odd positive integer, n=2m and p be an odd prime. For the decimation factor $d= rac{(p^{m}+1)(p^{m}+p-1)}{p+1}$, the cross-correlation between the p-ary m-sequence {tr1nt)} and its all decimated sequences {tr1ndt+l)} is investigated, where 0 ≤ l < gcd(d,pn-1) and α is a primitive element of Fpn. It is shown that the cross-correlation function takes values in {-1,-1±ipm|i=1,2,…p}. The result presented in this paper settles a conjecture proposed by Kim et al. in the 2012 IEEE International Symposium on Information Theory Proceedings paper (pp.1014-1018), and also improves their result.