On the Linear Ordering of Some Classes of Negacyclic and Cyclic Codes and Their Distance Distributions
Finite Fields and Their Applications
cyclic codes, negacyclic codes, finite fields, hamming distance, hamming weight, MacWilliams identity, repeated-root codes
We investigate negacyclic and cyclic codes of length ps over the finite field Fpa. Negacyclic codes of length ps are precisely the ideals of the chain ring Fpa [x] / 〈xp^s+1〉. This structure is then used to obtain the Hamming distance distribution of the class of such negacyclic codes, which also provides Hamming weight distributions and enumerations of several codes. An one-to-one correspondence between negacyclic and cyclic codes is established to carry accordingly those results of negacyclic codes to cyclic codes.
Dinh, Hai Q. (2008). On the Linear Ordering of Some Classes of Negacyclic and Cyclic Codes and Their Distance Distributions. Finite Fields and Their Applications 14(1), 22-40. doi: 10.1016/J.FFA.2007.07.001 Retrieved from https://digitalcommons.kent.edu/mathpubs/11