Anticodes for the Grassman and bilinear forms graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1995 English Publisher:Springer Science and Business Media LLCJournal:Designs, Codes and Cryptography, volume 6, pages 73-79 (issn: 0925-1022, eissn: 1573-7586,

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Authors: William J. Martin; X. J. Zhu;

doi: 10.1007/bf01390772

Anticodes for the Grassman and bilinear forms graphs

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Abstract

This paper presents anticodes in Grassmann graphs and bilinear forms graphs. A new proof of the result due to Chihara viz. ``Many infinite families of classical distance-regular graphs have no nontrivial perfect codes, including the Grassmann graphs and the bilinear forms graphs'' has been given for these two families. The main tool is Delsarte's anticode condition and the technique is an extension of an approach taken by Roos in the study of perfect codes in the Johnson graphs.

Related Organizations

University of Waterloo
Canada
University of Winnipeg
Canada

Keywords

Grassmann graphs, bilinear forms graphs, Delsarte's anticode condition, Linear codes (general theory)

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