A generalization of the Lee distance and error correcting codes

Authors:
S. Nishimura;T. Hiramatsu
Affiliations:
Department of Systems and Control Engineering, College of Engineering, Hosei University, Koganei, Tokyo 184-8584, Japan;Department of Systems and Control Engineering, College of Engineering, Hosei University, Koganei, Tokyo 184-8584, Japan
Venue:
Discrete Applied Mathematics
Year:
2008

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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.