In Beelen and Montanucci (Finite Fields Appl 52:10-29, 2018) and Giulietti and Korchmaros (Math Ann 343:229-245, 2009), Weierstrass semigroups at points of the Giulietti-Korchmaros curve chi were investigated and the sets of minimal generators were determined for all points in chi(F-q2) and chi(F-q6) \ chi(F-q2). This paper completes their work by settling the remaining cases, that is, for points in chi((F) over bar (q) )\ chi(F-q6). As an application to AG codes, we determine the dimensions and the lengths of duals of one-point codes from a point in chi(F-q7)\chi(F-q) and we give a bound on the Feng-Rao minimum distance d(O)(RD) . For q = 3 we provide a table that also reports the exact values of d(O)(RD) . As a further application we construct quantum codes from F-q7-rational points of the GK-curve.
AG codes from F-q7-rational points of the GK maximal curve
Timpanella, M
2021
Abstract
In Beelen and Montanucci (Finite Fields Appl 52:10-29, 2018) and Giulietti and Korchmaros (Math Ann 343:229-245, 2009), Weierstrass semigroups at points of the Giulietti-Korchmaros curve chi were investigated and the sets of minimal generators were determined for all points in chi(F-q2) and chi(F-q6) \ chi(F-q2). This paper completes their work by settling the remaining cases, that is, for points in chi((F) over bar (q) )\ chi(F-q6). As an application to AG codes, we determine the dimensions and the lengths of duals of one-point codes from a point in chi(F-q7)\chi(F-q) and we give a bound on the Feng-Rao minimum distance d(O)(RD) . For q = 3 we provide a table that also reports the exact values of d(O)(RD) . As a further application we construct quantum codes from F-q7-rational points of the GK-curve.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
