Proof of a conjecture of Sarwate and Pursley regarding pairs of binary m-sequences

Author

McGuire, Gary ; Calderbank, A.R.

Author_Institution

Dept. of Math., California Inst. of Technol., Pasadena, CA, USA

Volume

41

Issue

4

fYear

1995

fDate

7/1/1995 12:00:00 AM

Firstpage

1153

Lastpage

1155

Abstract

Binary m-sequences are maximal length sequences generated by shift registers of length m, that are employed in navigation, radar, and spread-spectrum communications systems, because of their crosscorrelation properties. It is well known that given a pair of distinct m-sequences, the crosscorrelation function must take on at least three values. The article considers crosscorrelation functions that take on exactly three values, and where these values are preferred in that they are small. The main result is a proof of a conjecture made by Sarwate and Pursley in 1980, that if m≡0 (mod 4) then there are no preferred pairs of binary m-sequences. The proof makes essential use of a deep theorem of McEliece (1971) that restricts the possible weights that can occur in a binary cyclic code

Keywords

binary sequences; correlation methods; cyclic codes; McEliece deep theorem; Sarwate/Pursley conjecture; binary cyclic code; binary m-sequences; code weights; crosscorrelation function; crosscorrelation properties; maximal length sequences; navigation; proof; radar; shift registers; spread-spectrum communications systems; Autocorrelation; Communication systems; Navigation; Periodic structures; Shift registers; Spread spectrum radar;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.391260

Filename

391260