TY  - JOUR
T1  - The root diagram for one-point AG codes arising from certain curves with separated variables
AU  - Fornasiero, Federico
AU  - Tizziotti, Guilherme
PY  - 2018
DA  - May
DO  - 10.13069/jacodesmath.423733
JF  - Journal of Algebra Combinatorics Discrete Structures and Applications
PB  - iPeak Academy
WT  - DergiPark
SN  - 2148-838X
SP  - 71
EP  - 83
VL  - 5
IS  - 2
LA  - en
AB  - Heegard, Little and Saints introduced in [8] an encoding algorithm for a class of AG codes via Gröbnerbasis more compact compared with the usual encoding via generator matrix. So, knowing that themain 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 algorithmfor 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 certaincurves with separated variables that has certain special automorphism and a Weierstrass semigroupgenerated by two elements. Such family of curves includes the norm-trace curve, among other curveswith recent applications in coding theory.
KW  - AG codes
KW  - Gröbner basis
KW  - Root diagram
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UR  - https://doi.org/10.13069/jacodesmath.423733
L1  - https://dergipark.org.tr/en/download/article-file/472470
ER  -