DocumentCode
873262
Title
Codes over algebraic integer rings of cyclotomic fields
Author
Fan, Yun ; Gao, Ying
Author_Institution
Dept. of Math., Wuhan Univ., China
Volume
50
Issue
1
fYear
2004
Firstpage
194
Lastpage
200
Abstract
Regarding any finite field as a residue field of the algebraic integer ring of a cyclotomic field, we select a system of representatives in the ring with minimal Manhattan metric, and introduce a Mannheim weight on the finite field. The linear codes over the finite field with the Mannheim weight are discussed. A geometric method to compute the representatives in Gaussian integers is provided.
Keywords
Gaussian distribution; algebraic geometric codes; linear codes; minimisation; Gaussian integer representatives; Mannheim weight; algebraic integer ring; cyclotomic field; finite field; geometric method; linear codes; minimal Manhattan metric; residue field; Constellation diagram; Error correction; Error correction codes; Euclidean distance; Galois fields; Lattices; Linear code; Mathematics; Multidimensional systems;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2003.821983
Filename
1262628
Link To Document