The root diagram for one-point AG codes arising from certain curves with separated variables

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Federico Fornasiero¹  Guilherme Tizziotti² 

[1] Department of Mathematics, Universidade Federal de Pernambuco;Department of Mathematics, Universidade Federal de Uberlândia

关键词: AG codes;    Gröbner basis;    Root diagram;   

DOI  :  10.13069/jacodesmath.423733

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

Heegard, Little and Saints introduced in [8] an encoding algorithm for a class of AG codes via Gröbner basis more compact compared with the usual encoding via generator matrix. So, knowing that the main drawback of Gröbner basis is the high computational cost required for its calculation, in [12], the same authors introduced the concept of root diagram that allows the construction of an algorithm for computing a Gröbner basis with a lower complexity for one-point Hermitian codes. In [4], Farrán, Munuera, Tizziotti and Torres extended the results obtained in [12] for codes on norm-trace curves. In this work we generalize these results by constructing the root diagram for codes arising from certain curves with separated variables that has certain special automorphism and a Weierstrass semigroup generated by two elements. Such family of curves includes the norm-trace curve, among other curves with recent applications in coding theory.

【 授权许可】

CC BY