Complete Distances of All Negacyclic Codes of Length $2^{s}$ Over $\BBZ _{2^{a}}$

Abstract

Various kinds of distances of all negacyclic codes of length 2^s over Zopf₂ ^a are completely determined. Using our structure theorems of negacyclic codes of length 2 ^s over Zopf₂ ^a, 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 2^s over Zopf₂ ^a , where lambda is any unit of Zopf₂ ^a with the form 4k-1. We establish the Hamming, homogeneous, Lee, and Euclidean distances of all such constacyclic codes