Minimal codewords in Norm-Trace codes

Daniele Bartoli; Matteo Bonini; Marco Timpanella

doi:10.48550/arXiv.2211.02329

Minimal codewords in Norm-Trace codes

Daniele Bartoli, Matteo Bonini, Marco Timpanella

Publikation: Working paper/Preprint › Preprint

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Abstract

In this paper, we consider the affine variety codes obtained evaluating the polynomials $by=a_kx^k+\dots+a_1x+a_0$, $b,a_i\in\mathbb{F}_{q^r}$, at the affine $\F_{q^r}$-rational points of the Norm-Trace curve. In particular, we investigate the weight distribution and the set of minimal codewords. Our approach, which uses tools of algebraic geometry, is based on the study of the absolutely irreducibility of certain algebraic varieties.

Originalsprog	Engelsk
Udgiver	arXiv
Antal sider	14
DOI	https://doi.org/10.48550/arXiv.2211.02329
Status	Udgivet - 4 nov. 2022

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math.AG
cs.IT
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10.48550/arXiv.2211.02329

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N2 - In this paper, we consider the affine variety codes obtained evaluating the polynomials $by=a_kx^k+\dots+a_1x+a_0$, $b,a_i\in\mathbb{F}_{q^r}$, at the affine $\F_{q^r}$-rational points of the Norm-Trace curve. In particular, we investigate the weight distribution and the set of minimal codewords. Our approach, which uses tools of algebraic geometry, is based on the study of the absolutely irreducibility of certain algebraic varieties.

AB - In this paper, we consider the affine variety codes obtained evaluating the polynomials $by=a_kx^k+\dots+a_1x+a_0$, $b,a_i\in\mathbb{F}_{q^r}$, at the affine $\F_{q^r}$-rational points of the Norm-Trace curve. In particular, we investigate the weight distribution and the set of minimal codewords. Our approach, which uses tools of algebraic geometry, is based on the study of the absolutely irreducibility of certain algebraic varieties.

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KW - Norm-trace curve

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KW - Weight spectrum

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Minimal codewords in Norm-Trace codes

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