Minimum distance of elliptic codes
type: Item
instance of: scholarly article
title: Minimum distance of elliptic codes
zbMATH Open document ID: 0758.94014
DOI: 10.1016/0001-8708(92)90029-K
author: M. Amin Shokrollahi
published in: Advances in Mathematics
publication date: 1992-09-27T00:00:00Z
review text: The author examine three series of linear codes arising from elliptic curves. An \((n,k,d)\) code defined over an elliptic curve is almost maximum distance separable one that is \(d=n-k+1\) or \(d=n-k\). One of the most important properties of an elliptic function field defined over a fixed finite field \(Q\) is the fact that there is a bijection from its class group onto its set of prime divisors of degree one. This map is used in this paper to compute the minimal distance of the above-mentioned family of codes. In almost all cases these codes are not maximum distance separable, so \(d=n-k\). It is interesting that the MDS codes one obtains in the ``trivial'' cases belong to the class of generalized Reed-Solomon codes.
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 14Q99
Mathematics Subject Classification ID: 94B15
zbMATH DE Number: 62676
zbMATH Keywords: maximum distance separable codes
zbMATH Keywords: elliptic curves
zbMATH Keywords: elliptic function field
zbMATH Keywords: minimal distance
zbMATH Keywords: MDS codes
zbMATH Keywords: generalized Reed-Solomon codes
reviewed by: Ákos G. Horváth
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 62676