On the symmetry group of extended perfect binary codes of length $n+1$ and rank $n-\log(n+1)+2$

Olof Heden; Fabio Pasticci; Thomas Westerbäck

doi:10.3934/amc.2012.6.121

Article Contents

2012, Volume 6, Issue 2: 121-130. Doi: 10.3934/amc.2012.6.121

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On the symmetry group of extended perfect binary codes of length $n+1$ and rank $n-\log(n+1)+2$

1.
Department of Mathematics, KTH, S-100 44 Stockholm
2.
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli, 1, I-06123 Perugia

Received: January 2011

Revised: August 2011

Published: May 2012

Abstract / Introduction Related Papers Cited by

Abstract

It is proved that for every integer $n=2^k-1$, with $k\geq5$, there exists a perfect code $C$ of length $n$, of rank $r=n-\log(n+1)+2$ and with a trivial symmetry group. This result extends an earlier result by the authors that says that for any length $n=2^k-1$, with $k\geq5$, and any rank $r$, with $n-\log(n+1)+3\leq r\leq n-1$ there exist perfect codes with a trivial symmetry group.

Keywords:

Perfect codes,
symmetry group.

Mathematics Subject Classification: Primary: 94B25.

Citation:

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References

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