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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 1

On the covering radii of a class of binary primitive cyclic codes

Seher Tutdere(BALIKESIR UNIVERSITY)0000-0001-5645-8174
Pages
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Publication Date
2022-02-14
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This new class of cyclic codes covers that of Kavut and Tutdere.

📌 3 Key Takeaways

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Objective & Hypothesis:In 2019, Kavut and Tutdere proved that the covering radii of a class of primitive binary cyclic codes with minimum distance greater than or equal to $r+2$ is $r$, where $r$ is an odd integer, under some assumptions.
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Key Findings & Data:We here show that the covering radii $R$ of a class of primitive binary cyclic codes with minimum distance strictly greater than $\ell$ satisfy $r\leq R \leq \ell$, where $\ell,r$ are some integers, with $\ell$ being odd, depending on the given code.
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Conclusion & Impact:This new class of cyclic codes covers that of Kavut and Tutdere.
🔬Design:Research Article
📍Scope:2019 Verileri
⚙️Variables:cyclic code · covering radius · finite field

Abstract

In 2019, Kavut and Tutdere proved that the covering radii of a class of primitive binary cyclic codes with minimum distance greater than or equal to $r+2$ is $r$, where $r$ is an odd integer, under some assumptions. We here show that the covering radii $R$ of a class of primitive binary cyclic codes with minimum distance strictly greater than $\ell$ satisfy $r\leq R \leq \ell$, where $\ell,r$ are some integers, with $\ell$ being odd, depending on the given code. This new class of cyclic codes covers that of Kavut and Tutdere.

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Cite This Article

Tutdere, S. (2022). On the covering radii of a class of binary primitive cyclic codes. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 1. https://doi.org/10.15672/hujms.881649

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