On a relation between GAG codes and AG codes

Abstract

In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely, we show that a GAG code is contained (up to isomorphism) in a suitable AG code. Next we recall the concept of an N1N2-automorphism group, a subgroup of the automorphism group of a GAG code. With the use of the relation we obtained between these two classes of codes, we show that the N1N2-automorphism group is a subgroup of the automorphism group of an AG code.

Keywords

• algebraic geometry codes
• generalized algebraic geometry codes
• geometric goppa codes
• code automorphisms
• algebraic function fields
• primary 94b27
• secondary 14h05, 14g50