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Journals / Sakarya University Journal of Science / 2026 / Volume: 23 Issue: 3

LCD codes and LCP of codes from units of group rings

Mehmet Emin Köroğlu(YILDIZ TEKNİK ÜNİVERSİTESİ)0000-0002-9173-4944
Pages
—
Publication Date
2019-06-01
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AI Summary & Key Takeaways

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

We also proposed a consruction of linear complementary pair (LCP) of codes.

📌 3 Key Takeaways

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Objective & Hypothesis:A linear code with complementary dual (LCD) is a linear code such that LCD codes are of great importance due to their wide range of applications in consumer electronics, storage systems and cryptography.
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Key Findings & Data:Group rings have a rich source of units.
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Conclusion & Impact:We also proposed a consruction of linear complementary pair (LCP) of codes.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:group rings · unit derived codes · LCD codes

Abstract

A linear code with complementary dual (LCD) is a linear code such that LCD codes are of great importance due to their wide range of applications in consumer electronics, storage systems and cryptography. Group rings have a rich source of units. Also the well-known structural linear codes such as cyclic codes are within the family of group ring codes. Thus, group rings offer an affluent source for structural codes that may lead to linear codes with good properties. In this work, we derive a condition for codes obtained from units of group rings to be LCD. We show that a special decomposition of group rings meet the LCD condition. We also proposed a consruction of linear complementary pair (LCP) of codes.

Özet

A linear code with complementary dual (LCD) is a linear code such that LCD codes are of great importance due to their wide range of applications in consumer electronics, storage systems and cryptography. Group rings have a rich source of units. Also the well-known structural linear codes such as cyclic codes are within the family of group ring codes. Thus, group rings offer an affluent source for structural codes that may lead to linear codes with good properties. In this work, we derive a condition for codes obtained from units of group rings to be LCD. We show that a special decomposition of group rings meet the LCD condition. We also proposed a consruction of linear complementary pair (LCP) of codes.

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Cite This Article

Köroğlu, M. E. (2019). LCD codes and LCP of codes from units of group rings. Sakarya University Journal of Science, Volume: 23 Issue: 3. https://doi.org/10.16984/saufenbilder.459123

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References (1)

  1. J. L. Massey, “Linear codes with complementary duals,” Discrete Math, vol. 106, pp. 337–342, 1992.[2] J. L. Massey, “Reversible codes,” Information and Control, vol. 7, pp. 369–380, 1964.[3] N. Sendrier, “Linear codes with complementary duals meet the Gilbert-Varshamov bound,” Discrete Math, vol. 285, pp. 345-347, 2004.[4] C. P. Milies, K.S. Sudarshan, “An introduction to group rings,” vol.1. Springer, Nedherlands, 2002.[5] P. Hurley, T. Hurley, “Codes from zero-divisors and units in group rings,” Int. J. Inf. Coding Theory vol. 1 pp. 57-87, 2009.