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

#### Federico Fornasiero [1] , Guilherme Tizziotti [2]

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.
AG codes, Gröbner basis, Root diagram
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Primary Language en Engineering Articles Author: Federico Fornasiero Orcid: 0000-0003-1026-0546Author: Guilherme Tizziotti Publication Date : May 15, 2018
 Bibtex @research article { jacodesmath423733, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2018}, volume = {5}, pages = {71 - 83}, doi = {10.13069/jacodesmath.423733}, title = {The root diagram for one-point AG codes arising from certain curves with separated variables}, key = {cite}, author = {Fornasiero, Federico and Tizziotti, Guilherme} } APA Fornasiero, F , Tizziotti, G . (2018). The root diagram for one-point AG codes arising from certain curves with separated variables . Journal of Algebra Combinatorics Discrete Structures and Applications , 5 (2) , 71-83 . DOI: 10.13069/jacodesmath.423733 MLA Fornasiero, F , Tizziotti, G . "The root diagram for one-point AG codes arising from certain curves with separated variables" . Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 71-83 Chicago Fornasiero, F , Tizziotti, G . "The root diagram for one-point AG codes arising from certain curves with separated variables". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 71-83 RIS TY - JOUR T1 - The root diagram for one-point AG codes arising from certain curves with separated variables AU - Federico Fornasiero , Guilherme Tizziotti Y1 - 2018 PY - 2018 N1 - doi: 10.13069/jacodesmath.423733 DO - 10.13069/jacodesmath.423733 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 71 EP - 83 VL - 5 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.423733 UR - https://doi.org/10.13069/jacodesmath.423733 Y2 - 2018 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications The root diagram for one-point AG codes arising from certain curves with separated variables %A Federico Fornasiero , Guilherme Tizziotti %T The root diagram for one-point AG codes arising from certain curves with separated variables %D 2018 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 5 %N 2 %R doi: 10.13069/jacodesmath.423733 %U 10.13069/jacodesmath.423733 ISNAD Fornasiero, Federico , Tizziotti, Guilherme . "The root diagram for one-point AG codes arising from certain curves with separated variables". Journal of Algebra Combinatorics Discrete Structures and Applications 5 / 2 (May 2018): 71-83 . https://doi.org/10.13069/jacodesmath.423733 AMA Fornasiero F , Tizziotti G . The root diagram for one-point AG codes arising from certain curves with separated variables. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(2): 71-83. Vancouver Fornasiero F , Tizziotti G . The root diagram for one-point AG codes arising from certain curves with separated variables. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(2): 71-83.

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