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Dergiler / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2026 / Volume: 37 Issue: 4

ON PERFECT CODES IN THE LEE-ROSENBLOOM-TSFASMAN-JAIN METRIC

Merve Bulut Yılgör(YILDIZ TECHNICAL UNIVERSITY)0000-0001-6842-1109
Fatih Demirkale(YILDIZ TECHNICAL UNIVERSITY)0000-0002-6114-1291
Sayfa
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Yayın Tarihi
2019-12-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Lastly, we obtain non-existence results on w-perfect linear codes over Z_p for 2≤w≤4.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we study perfect codes in the Lee-Rosenbloom-Tsfasman-Jain (LRTJ) metric over the finite field Z_p.
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Temel Bulgular & Veri:We begin by deriving some new upper bounds focusing on the number of parity check digits for linear codes correcting all error vectors of LRTJ weight up to w, 1≤w≤4.
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Sonuç & Katkı:Lastly, we obtain non-existence results on w-perfect linear codes over Z_p for 2≤w≤4.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Linear codes · perfect codes · LRTJ weight

Abstract

In this paper, we study perfect codes in the Lee-Rosenbloom-Tsfasman-Jain (LRTJ) metric over the finite field Z_p. We begin by deriving some new upper bounds focusing on the number of parity check digits for linear codes correcting all error vectors of LRTJ weight up to w, 1≤w≤4. Furthermore, we establish sufficient conditions for the existence of perfect codes correcting all error vectors with certain weights. We also search for linear codes which attain these bounds to determine the possible parameters of perfect codes. Moreover, we derive parity check matrices corresponding linear codes correcting all error vectors of LRTJ weight 1 over Z_p, and correcting all error vectors of LRTJ weight up to 2 over Z_3 and Z_11. We also construct perfect codes for these cases. Lastly, we obtain non-existence results on w-perfect linear codes over Z_p for 2≤w≤4.

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Bu Makaleye Atıf Yap

Yılgör, M. B., Demirkale, F. (2019). ON PERFECT CODES IN THE LEE-ROSENBLOOM-TSFASMAN-JAIN METRIC. Sigma Mühendislik ve Fen Bilimleri Dergisi, Volume: 37 Issue: 4. https://ajindex.com/articles/1344970

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Kaynakça (16)

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