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AG codes from Fq7-rational points of the GK maximal curve.
- Source :
-
Applicable Algebra in Engineering, Communication & Computing . Jul2023, Vol. 34 Issue 4, p629-648. 20p. - Publication Year :
- 2023
-
Abstract
- In Beelen and Montanucci (Finite Fields Appl 52:10–29, 2018) and Giulietti and Korchmáros (Math Ann 343:229–245, 2009), Weierstrass semigroups at points of the Giulietti–Korchmáros curve X were investigated and the sets of minimal generators were determined for all points in X (F q 2) and X (F q 6) \ X (F q 2) . This paper completes their work by settling the remaining cases, that is, for points in X (F ¯ q) \ X (F q 6) . As an application to AG codes, we determine the dimensions and the lengths of duals of one-point codes from a point in X (F q 7) \ X (F q) and we give a bound on the Feng–Rao minimum distance d ORD . For q = 3 we provide a table that also reports the exact values of d ORD . As a further application we construct quantum codes from F q 7 -rational points of the GK-curve. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 34
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 164263789
- Full Text :
- https://doi.org/10.1007/s00200-021-00519-2