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Perfect Mannheim, Lipschitz and Hurwitz weight codes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2014 (English)In: Mathematical Communications, ISSN 1331-0623, E-ISSN 1848-8013, Vol. 19, no 2, 253-276 p.Article in journal (Refereed) Published
Abstract [en]

The set of residue classes modulo an element pi in the rings of Gaussian integers, Lipschitz integers and Hurwitz integers, respectively, is used as alphabets to form the words of error correcting codes. An error occurs as the addition of an element in a set E to the letter in one of the positions of a word. If epsilon is a group of units in the original rings, then we obtain the Mannheim, Lipschitz and Hurwitz metrics, respectively. Some new perfect 1-error-correcting codes in these metrics are constructed. The existence of perfect 2-error-correcting codes is investigated by computer search.

Place, publisher, year, edition, pages
2014. Vol. 19, no 2, 253-276 p.
Keyword [en]
block codes, Lipschitz distance, Mannheim distance, perfect code
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-158394ISI: 000345431400004OAI: oai:DiVA.org:kth-158394DiVA: diva2:778883
Note

QC 20150112

Available from: 2015-01-12 Created: 2015-01-07 Last updated: 2017-12-05Bibliographically approved

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