Title :
Near Orders and Codes
Author :
Carvalho, Cìcero ; Munuera, Carlos ; Silva, Ercilio Da ; Torres, Fernando
Author_Institution :
Faculdade de Matematica, Univ. Fed. de Uberlandia
fDate :
5/1/2007 12:00:00 AM
Abstract :
Hoslashholdt, van Lint, and Pellikaan used order functions to construct codes by means of Linear Algebra and Semigroup Theory only. However, Geometric Goppa codes that can be represented by this method are mainly those based on just one point. In this correspondence, we introduce the concept of near order function with the aim of generalizing this approach in such a way that a wider family of Geometric Goppa codes can be studied on a more elementary setting
Keywords :
Goppa codes; geometric codes; linear algebra; geometric Goppa codes; linear algebra; order function; semigroup theory; Error correction codes; Galois fields; Linear algebra; Mathematics; Algebraic geometric Goppa (GG) codes; Weierstrass semigroups; error-correcting codes; order function;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2007.894663
