Perfect Mannheim, Lipschitz and Hurwitz weight codes
2014 (English)In: Mathematical Communications, ISSN 1331-0623, Vol. 19, no 2, 253-276 p.Article in journal (Refereed) Published
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.
block codes, Lipschitz distance, Mannheim distance, perfect code
IdentifiersURN: urn:nbn:se:kth:diva-158394ISI: 000345431400004OAI: oai:DiVA.org:kth-158394DiVA: diva2:778883
QC 201501122015-01-122015-01-072015-01-12Bibliographically approved