Original scientific paper

Perfect Mannheim, Lipschitz and Hurwitz weight codes

Murat Güzeltepe ; Department of Mathematics, Sakarya University, Sakarya,Turkey
Olof Heden ; Department of Mathematics, Stockholm, Sweden

Abstract

The set of residue classes modulo an element 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 E 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.

Keywords

block codes; Lipschitz distance; Mannheim distance; perfect code

Hrčak ID:

129575

URI

https://hrcak.srce.hr/129575

Publication date:

5.12.2014.

Visits: 1.073 *