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Journals / TWMS Journal of Applied and Engineering Mathematics / 2012 / Volume: 2 Issue: 2

GENERALIZATION OF THE LEE WEIGHT TO Ζpk

B. Yıldız(Department of Mathematics, Fatih University, 34500, Istanbul, Turkey)
Z. Ödemiş Özger(Department of Mathematics, Fatih University, 34500, Istanbul, Turkey)
Pages
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Publication Date
2012-12-01
DOI
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AI Summary & Key Takeaways

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

Unlike the case of generalized Lee weight, we define a distance-preserving Gray map from Zpk , extended Lee distance to F p k−1 p , Hamming distance , thus making our extension practical for coding theory purposes.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce a new extension of the Lee weight to Zpk and later to Galois rings GR p k , m .
📊
Key Findings & Data:The weight we define is a non-homogeneous weight and is different than the one that is generally labeled as “generalized Lee weight”.
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Conclusion & Impact:Unlike the case of generalized Lee weight, we define a distance-preserving Gray map from Zpk , extended Lee distance to F p k−1 p , Hamming distance , thus making our extension practical for coding theory purposes.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Lee weight · extended · Gray map

Abstract

We introduce a new extension of the Lee weight to Zpk and later to Galois rings GR p k , m . The weight we define is a non-homogeneous weight and is different than the one that is generally labeled as “generalized Lee weight”. Unlike the case of generalized Lee weight, we define a distance-preserving Gray map from Zpk , extended Lee distance to F p k−1 p , Hamming distance , thus making our extension practical for coding theory purposes.

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Cite This Article

Yıldız, B., Özger, Z. Ö. (2012). GENERALIZATION OF THE LEE WEIGHT TO Ζpk. TWMS Journal of Applied and Engineering Mathematics, Volume: 2 Issue: 2. https://ajindex.com/articles/1604689

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