AU - Mohammadi, R.
TI - One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes
PT - JOURNAL ARTICLE
TA - IJMSI
JN - IJMSI
VO - 16
VI - 1
IP - 1
4099 - http://ijmsi.ir/article-1-1284-en.html
4100 - http://ijmsi.ir/article-1-1284-en.pdf
SO - IJMSI 1
ABĀ - 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 yl = 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).
CP - IRAN
IN - Department of Mathematics, Tarbiat Modares University, Tehran, Iran.
LG - eng
PB - IJMSI
PG - 65
PT - Research paper
YR - 2021