Two generalizations on the minimum Hamming distance of repeated-root constacyclic codes
نویسندگان
چکیده
We study constacyclic codes, of length np and 2np, that are generated by the polynomials (x+γ) and (x−ξ)(x+ξ) respectively, where x+γ, x−ξ and x+ξ are irreducible over the alphabet Fpa . We generalize the results of [5], [6] and [7] by computing the minimum Hamming distance of these codes. As a particular case, we determine the minimum Hamming distance of cyclic and negacyclic codes, of length 2p, over a finite field of characteristic p.
منابع مشابه
Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes
Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR(p,m) and generating sets for its ideals are considered. It is shown that these generating sets are strong Groebner bases. A method for finding ...
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عنوان ژورنال:
- CoRR
دوره abs/0906.4008 شماره
صفحات -
تاریخ انتشار 2009