Complete Mutually Orthogonal Golay Complementary Sets From Reed–Muller Codes

Author

Rathinakumar, Appuswamy ; Chaturvedi, Ajit Kumar

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., La Jolla, CA

Volume

54

Issue

3

fYear

2008

fDate

3/1/2008 12:00:00 AM

Firstpage

1339

Lastpage

1346

Abstract

Recently Golay complementary sets were shown to exist in the subsets of second-order cosets of a q-ary generalization of the first-order Reed-Muller (RM) code. We show that mutually orthogonal Golay complementary sets can also be directly constructed from second-order cosets of a q-ary generalization of the first-order RM code. This identification can be used to construct zero correlation zone (ZCZ) sequences directly and it also enables the construction of ZCZ sequences with special subsets.

Keywords

Golay codes; Reed-Muller codes; orthogonal codes; complete mutually orthogonal Golay complementary sets; first-order Reed-Muller code; g-ary generalization; second-order cosets; zero correlation zone sequences; Bit error rate; Boolean functions; Computational complexity; IP networks; Multiaccess communication; Multipath channels; OFDM; Satellites; Time varying systems; Ultra wideband technology; Complementary sets; Reed–Muller (RM) codes; generalized Boolean function; mutually orthogonal Golay complementary sets; zero correlation zone (ZCZ) sequences;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2007.915980

Filename

4455756