Zeros of polynomials over finite principal ideal rings
نویسندگان
چکیده
منابع مشابه
MDS codes over finite principal ideal rings
The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(pe, l) (including Zpe). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite chain rings. We also construct MDS self-dual...
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In this paper, we give an important isomorphism between contacyclic codes and cyclic codes,over finite principal ideal rings.Necessary and sufficient conditions for the existence of non-trivial cyclic self-dual codes over finite principal ideal rings are given.
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Let R be a finite principal left ideal ring. Via a total ordering of the ring elements and an ordered basis a lexicographic ordering of the module R is produced. This is used to set up a greedy algorithm that selects vectors for which all linear combination with the previously selected vectors satisfy a pre-specified selection property and updates the to-be-constructed code to the linear hull o...
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In this article we consider the intersection graph G(R) of nontrivial proper ideals of a finite commutative principal ideal ring R with unity 1. Two distinct ideals are adjacent if they have non-trivial intersection. We characterize when the intersection graph is complete, bipartite, planar, Eulerian or Hamiltonian. We also find a formula to calculate the number of ideals in each ring and the d...
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Let R be a finite principal ideal ring and S the Galois extension of R of degree m. For k and k, positive integers we determine the number of free S-linear codes B of length l with the property k = rankS(B) and k = rankR(B∩R). This corrects a wrong result [1, Theorem 6] which was given in the case of finite fields.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0360541-8