On a conjectured ideal autocorrelation sequence and a related triple-error correcting cyclic code

Author

Chang, Anchung ; Gaal, Peter ; Golomb, Solomon W. ; Gong, Guang ; Helleseth, Tor ; Kumar, P. Vijay

Author_Institution

Space & Commun., Hughes Aircraft Co., Los Angeles, CA, USA

Volume

46

Issue

2

fYear

2000

fDate

3/1/2000 12:00:00 AM

Firstpage

680

Lastpage

687

Abstract

In a previous paper, No, Golomb, Gong, Lee and Gaal (see ibid., vol.44, p.814-17, 1998) conjectured that certain binary sequences having a simple trace description possess the ideal autocorrelation property. In the present paper it is shown that each such sequence is balanced and, moreover, that the dual of the linear cyclic code generated by the sequence and its cyclic shifts, is a triple-error correcting code having the same weight distribution as the triple-error correcting Bose-Chaudhuri-Hocquenghem (BCH) code. This cyclic code also contains a cyclic subcode that yields a new family of sequences having the same size and correlation parameters as does the family of Gold sequences

Keywords

binary sequences; correlation methods; cyclic codes; error correction codes; linear codes; BCH code; Bose-Chaudhuri-Hocquenghem code; Gold sequences; binary sequences; correlation parameters; cyclic shifts; cyclic subcode; ideal autocorrelation sequence; linear cyclic code; trace description; triple-error correcting cyclic code; weight distribution; Autocorrelation; Binary sequences; Combinatorial mathematics; Councils; Cryptography; Error correction; Error correction codes; Galois fields; Gold; Informatics;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.825842

Filename

825842