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Codes over algebraic integer rings of cyclotomic fields

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2 Author(s)
Yun Fan ; Dept. of Math., Wuhan Univ., China ; Ying Gao

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.

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Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 1 )