Δ-sequences and Evaluation Codes Defined by Plane Valuations at Infinity
نویسنده
چکیده
We introduce the concept of δ-sequence. A δ-sequence ∆ generates a well-ordered semigroup S in Z or R. We show how to construct (and compute parameters) for the dual code of any evaluation code associated with a weight function defined by ∆ from the polynomial ring in two indeterminates to a semigroup S as above. We prove that this is a simple procedure which can be understood by considering a particular class of valuations of function fields of surfaces, called plane valuations at infinity. We also give algorithms to construct an unlimited number of δ-sequences of the different existing types, and so this paper provides the tools to know and use a new large set of codes.
منابع مشابه
$\delta$-sequences and Evaluation Codes defined by Plane Valuations at Infinity
We introduce the concept of δ-sequence. A δ-sequence ∆ generates a well-ordered semigroup S in Z or R. We show how to construct (and compute parameters) for the dual code of any evaluation code associated with a weight function defined by ∆ from the polynomial ring in two indeterminates to a semigroup S as above. We prove that this is a simple procedure which can be understood by considering a ...
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We introduce the concept of δ-sequence. A δ-sequence ∆ generates a wellordered semigroup S in Z or R. We show how to construct (and compute parameters) for the dual code of any evaluation code associated with a weight function defined by ∆ from the polynomial ring in two indeterminates to a semigroup S as above. We prove that this is a simple procedure which can be understood by considering a p...
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