On linear equivalence and Phelps codes

Olof Heden; Martin Hessler

doi:10.3934/amc.2010.4.69

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2010, Volume 4, Issue 1: 69-81. Doi: 10.3934/amc.2010.4.69

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On linear equivalence and Phelps codes

Olof Heden^1, and
Martin Hessler^2,

1.
Department of Mathematics, KTH, Stockholm, Sweden S-100 44
2.
Department of Mathematics, University of Linkping, Linkping, Sweden S-581 83

Received: June 30, 2009

Revised: September 30, 2009

Published: January 2010

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Abstract

It is shown that all non-full-rank FRH-codes, a class of perfect codes we define in this paper, are linearly equivalent to perfect codes obtainable by Phelps' construction. Moreover, it is shown by an example that the class of perfect FRH-codes also contains perfect codes that are not obtainable by Phelps construction.

Keywords:

Perfect codes,
tilings.

Mathematics Subject Classification: Primary: 94B25.

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