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.
Institute of Electrical and Electronics Engineers
Dinh, Hai Q (2007). Complete Distances of All Negacyclic Codes of Length 2s Over Z2a. Institute of Electrical and Electronics Engineers 53(1) 147-161. doi: 10.1109/TIT.2006.887487. Retrieved from https://oaks.kent.edu/mathpubs/9