Title :
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
fDate :
3/1/2000 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
