DocumentCode
1552847
Title
The Nordstrom-Robinson code is algebraic-geometric
Author
Walker, Judy L.
Author_Institution
Dept. of Math. & Stat., Nebraska Univ., Lincoln, NE, USA
Volume
43
Issue
5
fYear
1997
fDate
9/1/1997 12:00:00 AM
Firstpage
1588
Lastpage
1593
Abstract
The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980s. There has also been an increased interest in the study of linear codes over finite rings. In a previous paper, we combined these two approaches to coding theory by introducing and studying algebraic-geometric codes over rings. We show that the Nordstrom-Robinson code is the image under the Gray mapping of an algebraic-geometric code over Z/4Z
Keywords
algebraic geometric codes; linear codes; Gray mapping; Nordstrom-Robinson code; algebraic geometry; algebraic-geometric codes; coding theory; finite fields; finite rings; linear codes; nonlinear image; Binary codes; Galois fields; Geometry; Hamming weight; Heart; Linear code; Mathematics; Statistics; Vectors;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.623154
Filename
623154
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