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On perfect p-ary codes of length p+1
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2008 (English)In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 46, no 1, 45-56 p.Article in journal (Refereed) Published
Abstract [en]

Let p be a prime number and assume p >= 5. We will use a result of L. Redei to prove, that every perfect 1-error correcting code C of length p + 1 over an alphabet of cardinality p, such that C has a rank equal to p and a kernel of dimension p - 2, will be equivalent to some Hamming code H. Further, C can be obtained from H, by the permutation of the symbols, in just one coordinate position.

Place, publisher, year, edition, pages
2008. Vol. 46, no 1, 45-56 p.
Keyword [en]
perfect codes, Redei theorem
URN: urn:nbn:se:kth:diva-17253DOI: 10.1007/s10623-007-9133-yISI: 000251609600004ScopusID: 2-s2.0-37149052190OAI: diva2:335296
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Heden, Olof
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