Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.29252/ijmsi
14
8888
13
en
jalali
1400
1
1
gregorian
2021
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1
16
1
online
1
fulltext
en
One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes
عمومى
General
پژوهشي
Research paper
<div style="text-align: justify;">We investigate one-point algebraic geometric codes C<sub>L</sub>(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation y<sup>l</sup> = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y<sup>4</sup> = x<sup>3</sup> +x and Picard curves given by the equations y<sup>3</sup> = x<sup>4</sup>-x and y3 = x<sup>4</sup> -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 F<sub>7<sup>2</sup></sub> 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 C<sub>L</sub>(D, G).</div>
Algebraic geometric codes, Maximal curves, Minimum distance, Goppa bound, Quantum error-correcting codes
65
76
http://ijmsi.ir/browse.php?a_code=A-10-3328-1&slc_lang=en&sid=1
R.
Mohammadi
rasool.mohammadi@modares.ac.ir
`10031947532846008123`

10031947532846008123
Yes
Department of Mathematics, Tarbiat Modares University.