Estimates of the distance distribution of codes and designs

Author

Askikhmin, A. ; Barg, Alexander ; Litsyn, Simon

Author_Institution

Lucent Technol. Bell Labs., Murray Hill, NJ, USA

Volume

47

Issue

3

fYear

2001

fDate

3/1/2001 12:00:00 AM

Firstpage

1050

Lastpage

1061

Abstract

We consider the problem of bounding the distance distribution for unrestricted block codes with known distance and/or dual distance. Applying the polynomial method, we provide a general framework for previously known results. We derive several upper and lower bounds both for finite length and for sequences of codes of growing length. Asymptotic results in the paper improve previously known estimates. In particular, we prove the best known bounds on the binomiality range of the distance spectrum of codes with a known dual distance

Keywords

binary sequences; block codes; error statistics; polynomials; spectral analysis; asymptotic results; binomiality range; code design; code distance; code length; constant weight codes; decoding error probability; distance distribution bounding; distance distribution estimates; distance spectrum; dual distance; finite length sequences; high rate codes; lower bound; unrestricted block codes; upper bound; Block codes; Error correction codes; Linear programming; Maximum likelihood decoding; Maximum likelihood detection; Performance analysis; Polynomials; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.915662

Filename

915662