Title :
Codes over algebraic integer rings of cyclotomic fields
Author :
Fan, Yun ; Gao, Ying
Author_Institution :
Dept. of Math., Wuhan Univ., China
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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2003.821983
