On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions

Authors:
Hai Q. Dinh
Affiliations:
Department of Mathematical Sciences, Kent State University, 4314 Mahoning Avenue, Warren, OH 44483, USA
Venue:
Finite Fields and Their Applications
Year:
2008

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Abstract

We investigate negacyclic and cyclic codes of length p^s over the finite field F"p"^"a. Negacyclic codes of length p^s are precisely the ideals of the chain ring F"p"^"a[x]. 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.