NEAR ORDERS ON HIGHER DIMENSIONAL VARIETIES
Rafael Peixoto
Universidade Estadual de Campinas - UNICAMP
Instituto de Matem´atica, Estat´ıstica e Computa¸c˜ao Cient´ıfica - IMECC Abstract. Goppa constructed codes based on algebraic curves; many au- thors generalize this construction based on higher dimensional varieties such as Hermitian varieties, Toric varieties, zero schemes of vector bundles, etc..
The study of these codes, which is based on resources from algebraic ge- ometry, is usually difficult. Høholdt, van Lint and Pellikaan presented a construction of codes by using linear algebra and semigroup theory only.
This construction is based on the concept of weight on algebras (over finite fields). Matsumoto noticed that the aforementioned construction allows us to work mainly with one-point Goppa codes. A similar picture for the case of two-points Goppa codes was worked out by using the concept of near weight. The very general concept of weight on an arbitrary variety was given by Geil, Pellikaan and Little. Here we will introduce the notion of near weighton arbitrary algebraic varieties.
References
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