Title

Complete Distances of All Negacyclic Codes of Length 2s Over Z2a

Publication Title

IEEE Transactions on Information Theory

Publication Date

1-2007

Document Type

Article

DOI

10.1109/TIT.2006.887487

Keywords

binary codes, chain rings, codes over finite rings, constacyclic codes, cyclic codes, euclidean distance, hamming distance, homogeneous distance, Lee distance, negacyclic codes, quarternary codes, repeated-root codes

Disciplines

Mathematics

Abstract

Various kinds of distances of all negacyclic codes of length 2s over Zopf2a are completely determined. Using our structure theorems of negacyclic codes of length 2s over Zopf2a, we first calculate the Hamming distances of all such negacyclic codes, which particularly lead to the Hamming weight distributions and Hamming weight enumerators of several codes. These Hamming distances are then used to obtain their homogeneous, Lee, and Euclidean distances. Our techniques are extendable to the more general class of constacyclic codes, namely, the lambda- constacyclic codes of length 2s over Zopf2a, where lambda is any unit of Zopf2a with the form 4k-1. We establish the Hamming, homogeneous, Lee, and Euclidean distances of all such constacyclic codes.

Publisher

Institute of Electrical and Electronics Engineers

Publisher Location

New York, NY


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