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The classification of some perfect codes
KTH, Superseded Departments, Mathematics.
2004 (English)In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 31, no 3, 313-318 p.Article in journal (Refereed) Published
Abstract [en]

Perfect 1-error correcting codes C in Z(2)(n), where n = 2(m) - 1, are considered. Let [C] denote the linear span of the words of C and let the rank of C be the dimension of the vector space [C]. It is shown that if the rank of C is n - m + 2 then C is equivalent to a code given by a construction of Phelps. These codes are, in case of rank n - m + 2, described by a Hamming code H and a set of MDS-codes D-h; h is an element of H, over an alphabet with four symbols. The case of rank n - m + 1 is much simpler: Any such code is a Vasil'ev code.

Place, publisher, year, edition, pages
2004. Vol. 31, no 3, 313-318 p.
Keyword [en]
perfect codes, error-correcting codes
National Category
Computer and Information Science Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-23166DOI: 10.1023/B:DESI.0000015891.01562.c1ISI: 000188923400009Scopus ID: 2-s2.0-1842638524OAI: oai:DiVA.org:kth-23166DiVA: diva2:341864
Note
QC 20100525 QC 20111031Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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