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<p>This paper studies skew constacyclic codes over a family of finite rings denoted by <i>B</i><sub><i>k</i></sub> to obtain quantum codes over the fields <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb{F}_{p^r}\)</EquationSource> </InlineEquation> and to construct Euclidean LCD skew constacyclic codes. The author investigates the structural properties of skew constacyclic codes over <i>B</i><sub><i>k</i></sub> using a decomposition approach, and also finds necessary and sufficient conditions for skew constacyclic codes that contain their duals. Finally, the author gives some examples of quantum codes obtained via the construction and LCD codes.</p>

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Skew Constacyclic Codes over a Family of Finite Rings and Their Applications to LCD and Quantum Codes

  • 期刊论文

  • 发表日期：

    2025年11月19日

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  • Abdullah Dertli

摘要

This paper studies skew constacyclic codes over a family of finite rings denoted by Bk to obtain quantum codes over the fields \(\mathbb{F}_{p^r}\) and to construct Euclidean LCD skew constacyclic codes. The author investigates the structural properties of skew constacyclic codes over Bk using a decomposition approach, and also finds necessary and sufficient conditions for skew constacyclic codes that contain their duals. Finally, the author gives some examples of quantum codes obtained via the construction and LCD codes.