New code upper bounds from the Terwilliger algebra and semidefinite programming

We give a new upper bound on the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. It is based on block-diagonalizing the Terwilliger algebra of the Hamming cube. The bound strengthens the Delsarte bound, and can be calculated with semidefinite programming in tim...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:IEEE transactions on information theory 2005-08, Vol.51 (8), p.2859-2866
1. Verfasser: Schrijver, A.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We give a new upper bound on the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. It is based on block-diagonalizing the Terwilliger algebra of the Hamming cube. The bound strengthens the Delsarte bound, and can be calculated with semidefinite programming in time bounded by a polynomial in n. We show that it improves a number of known upper bounds for concrete values of n and d. From this we also derive a new upper bound on the maximum size A(n,d,w) of a binary code of word length n, minimum distance at least d, and constant weight w, again strengthening the Delsarte bound and yielding several improved upper bounds for concrete values of n, d, and w
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2005.851748