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- Title
One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes .
- Authors
Mohammadi, Rasoul
- Abstract
We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation y l = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x³ + x and Picard curves given by the equations y3 = x4 − x and y³ = x4 − 1. As a result, we obtain exact value of minimum distance in several cases and get many records that don’t exist in MinT tables (tables of optimal parameters for linear codes), such as codes over F7² of dimension less than 36. Moreover, using maximal Hermitian curves and their sub-covers, we obtain a necessary and sufficient condition for self-orthogonality and Hermitian self-orthogonally of CL(D, G).
- Subjects
ERROR-correcting codes; LINEAR codes; ALGEBRAIC codes; EQUATIONS; MAXIMA &; minima
- Publication
Iranian Journal of Mathematical Sciences & Informatics, 2021, Vol 16, Issue 1, p65
- ISSN
1735-4463
- Publication type
Article
- DOI
10.29252/ijmsi.16.1.65