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• W2399717790 abstract "Let R be a Galois ring of characteristic $$p^a$$ , where p is a prime and a is a natural number. In this paper cyclic codes of arbitrary length n over R have been studied. The generators for such codes in terms of minimal degree polynomials of certain subsets of codes have been obtained. We prove that a cyclic code of arbitrary length n over R is generated by at most $$min{a, t+1}$$ elements, where $$t=max{deg(g(x))},$$ g(x) a generator. In particular, it follows that a cyclic code of arbitrary length n over finite fields is generated by a single element. Moreover, the explicit set of generators so obtained turns out to be a minimal strong Gröbner basis." @default.
• W2399717790 created "2016-06-24" @default.
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• W2399717790 date "2016-01-01" @default.
• W2399717790 modified "2023-09-23" @default.
• W2399717790 title "Cyclic Codes over Galois Rings" @default.
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• W2399717790 doi "https://doi.org/10.1007/978-3-319-29221-2_20" @default.
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