In this contribution, we will define an l-dimensional Lee distance which is a generalization of the Lee distance defined only over a prime field, and we will construct 2-error correcting codes for this distance. Our l-dimensional Lee distance can be defined not only over a prime field but also over any finite field. The ordinary Lee distance is just the one-dimensional Lee distance. Also the Mannheim or modular distances introduced by Huber are special cases of our distance.
%0 Journal Article
%1 Nishimura:2008
%A Nishimura, S.
%A Hiramatsu, T.
%D 2008
%J Discrete Applied Mathematics
%K Codierungstheorie Higher_dimensional_Lee_distance Mannheim_metric
%N 5
%P 588--595
%T A generalization of the Lee distance and error correcting codes
%U http://www.sciencedirect.com/science/article/B6TYW-4R2HKH4-1/1/fc6d78d6b62a316827bca54f7c0c0512
%V 156
%X In this contribution, we will define an l-dimensional Lee distance which is a generalization of the Lee distance defined only over a prime field, and we will construct 2-error correcting codes for this distance. Our l-dimensional Lee distance can be defined not only over a prime field but also over any finite field. The ordinary Lee distance is just the one-dimensional Lee distance. Also the Mannheim or modular distances introduced by Huber are special cases of our distance.
@article{Nishimura:2008,
abstract = { In this contribution, we will define an l-dimensional Lee distance which is a generalization of the Lee distance defined only over a prime field, and we will construct 2-error correcting codes for this distance. Our l-dimensional Lee distance can be defined not only over a prime field but also over any finite field. The ordinary Lee distance is just the one-dimensional Lee distance. Also the Mannheim or modular distances introduced by Huber are special cases of our distance.},
added-at = {2009-10-23T11:46:41.000+0200},
author = {Nishimura, S. and Hiramatsu, T.},
bdsk-url-1 = {http://www.sciencedirect.com/science/article/B6TYW-4R2HKH4-1/1/fc6d78d6b62a316827bca54f7c0c0512},
biburl = {https://www.bibsonomy.org/bibtex/296ffd5f89d377856acdf5a08dc83b876/keinstein},
date-added = {2008-04-24 16:58:25 +0200},
date-modified = {2009-04-01 11:30:27 +0200},
groups = {public},
interhash = {74e752d8a3f0e256a9e68240e4e7e6ba},
intrahash = {96ffd5f89d377856acdf5a08dc83b876},
journal = {Discrete Applied Mathematics},
keywords = {Codierungstheorie Higher_dimensional_Lee_distance Mannheim_metric},
number = 5,
pages = {588--595},
read = {Yes},
timestamp = {2013-01-20T19:14:59.000+0100},
title = {A generalization of the Lee distance and error correcting codes},
ty = {JOUR},
url = {http://www.sciencedirect.com/science/article/B6TYW-4R2HKH4-1/1/fc6d78d6b62a316827bca54f7c0c0512},
username = {keinstein},
volume = 156,
year = 2008
}