Determining hulls of generalized Reed-Solomon codes from algebraic geometry codes

Fuente: arXiv
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Main Authors: Jia, Xue, Yue, Qin, Sun, Huan, Sui, Junzhen
Format: Preprint
Published: 2024
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author Jia, Xue
Yue, Qin
Sun, Huan
Sui, Junzhen
author_facet Jia, Xue
Yue, Qin
Sun, Huan
Sui, Junzhen
contents In this paper, we provide conditions that hulls of generalized Reed-Solomon (GRS) codes are also GRS codes from algebraic geometry codes. If the conditions are not satisfied, we provide a method of linear algebra to find the bases of hulls of GRS codes and give formulas to compute their dimensions. Besides, we explain that the conditions are too good to be improved by some examples. Moreover, we show self-orthogonal and self-dual GRS codes.
format Preprint
id arxiv_https___arxiv_org_abs_2401_13394
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Determining hulls of generalized Reed-Solomon codes from algebraic geometry codes
Jia, Xue
Yue, Qin
Sun, Huan
Sui, Junzhen
Information Theory
In this paper, we provide conditions that hulls of generalized Reed-Solomon (GRS) codes are also GRS codes from algebraic geometry codes. If the conditions are not satisfied, we provide a method of linear algebra to find the bases of hulls of GRS codes and give formulas to compute their dimensions. Besides, we explain that the conditions are too good to be improved by some examples. Moreover, we show self-orthogonal and self-dual GRS codes.
title Determining hulls of generalized Reed-Solomon codes from algebraic geometry codes
topic Information Theory
url https://arxiv.org/abs/2401.13394