IEICE TRANSACTIONS on Fundamentals
Cross-Correlation between a p-Ary m-Sequence and Its All Decimated Sequences for $d= rac{(p^{m}+1)(p^{m}+p-1)}{p+1}$
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 {tr1n(αt)} and its all decimated sequences {tr1n(αdt+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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.4 pp.964-969
- Publication Date
- 2014/04/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E97.A.964
- Type of Manuscript
- PAPER
- Category
- Information Theory
Authors
Yongbo XIA
South-Central University for Nationalities,University of Bergen
Shaoping CHEN
South-Central University for Nationalities
Tor HELLESETH
University of Bergen
Chunlei LI
University of Bergen
Keyword
Latest Issue
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Yongbo XIA, Shaoping CHEN, Tor HELLESETH, Chunlei LI, "Cross-Correlation between a p-Ary m-Sequence and Its All Decimated Sequences for $d= rac{(p^{m}+1)(p^{m}+p-1)}{p+1}$" in IEICE TRANSACTIONS on Fundamentals,
vol. E97-A, no. 4, pp. 964-969, April 2014, doi: 10.1587/transfun.E97.A.964.
Abstract: 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 {tr1n(αt)} and its all decimated sequences {tr1n(αdt+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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.964/_p
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@ARTICLE{e97-a_4_964,
author={Yongbo XIA, Shaoping CHEN, Tor HELLESETH, Chunlei LI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Cross-Correlation between a p-Ary m-Sequence and Its All Decimated Sequences for $d= rac{(p^{m}+1)(p^{m}+p-1)}{p+1}$},
year={2014},
volume={E97-A},
number={4},
pages={964-969},
abstract={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 {tr1n(αt)} and its all decimated sequences {tr1n(αdt+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.},
keywords={},
doi={10.1587/transfun.E97.A.964},
ISSN={1745-1337},
month={April},}
Copy
TY - JOUR
TI - Cross-Correlation between a p-Ary m-Sequence and Its All Decimated Sequences for $d= rac{(p^{m}+1)(p^{m}+p-1)}{p+1}$
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 964
EP - 969
AU - Yongbo XIA
AU - Shaoping CHEN
AU - Tor HELLESETH
AU - Chunlei LI
PY - 2014
DO - 10.1587/transfun.E97.A.964
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2014
AB - 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 {tr1n(αt)} and its all decimated sequences {tr1n(αdt+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.
ER -
English
