Proof of a Conjecture of Sarwate and Pursley Regarding Pairs of Binary m-Sequences

Journal Article

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. This correspondence 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 that restricts the possible weights that can occur in a binary cyclic code. © 1995 IEEE

Full Text

Duke Authors

Cited Authors

  • McGuire, G; Calderbank, AR

Published Date

  • January 1, 1995

Published In

Volume / Issue

  • 41 / 4

Start / End Page

  • 1153 - 1155

Electronic International Standard Serial Number (EISSN)

  • 1557-9654

International Standard Serial Number (ISSN)

  • 0018-9448

Digital Object Identifier (DOI)

  • 10.1109/18.391260

Citation Source

  • Scopus