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Dergiler / 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
Sayfa
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Yayın Tarihi
2022-02-14
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı:This new class of cyclic codes covers that of Kavut and Tutdere.
🔬Tür:Research Article
📍Kapsam:2019 Verileri
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (12)

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