Name:GAG-Codes
Description:On GAG-Codes and Geometric Goppa Codes
Abstract:Generalized algebraic geometry codes (for short GAG-code) have recently been proposed by Xing, Niederreiter and Lam [2].<BR/>The construction of these new linear codes is based on algebraic curves. In fact, they make essentially use of points of an algebraic curve over finite fields. This construction is quietly different from the one made by Goppa [1] which uses only rational points. For a subclass of GAG-codes, Picone and Spera [3,4] studied their automorphism groups.<BR/><BR/><BR/>More precisely, they consider GAG-codes constructed with points which are all of the same degree.<BR/><BR/><BR/>Here, we show how a GAG-code C(F;G;n) of this subclass can be thought as expansion code of a vectorial subspace of a geometric Goppa code C(D’,Con(G)) (also called AG-code). Moreover, it is proved that the n-automorphism group of C(F;G;n) is, up to isomorphism, a subgroup of the automorphism group of C(D’,Con(G)).<BR/><BR/><BR/><BR/><BR/><BR/><b>Software requirements</b>: Algebraic function fields and linear codes^
Created:2010-05-01
Last updated:2012-01-20
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