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<p>In this paper, we characterize the skew constacyclic codes of length <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\( p^s \)</EquationSource> </InlineEquation> over <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\( R_3= \mathbb {F}_{p^m}+u\mathbb {F}_{p^m}+{u^2}\mathbb {F}_{p^m}\)</EquationSource> </InlineEquation> for special automorphisms, where <i>p</i> is a prime, <i>m</i> is a positive integer, <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\( \mathbb {F}_{p^m} \)</EquationSource> </InlineEquation> is a finite field of cardinality <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\( p^m\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\( u^3=0. \)</EquationSource> </InlineEquation> First, we classify all skew constacyclic codes of length <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\( p^s \)</EquationSource> </InlineEquation> over <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\( R_3\)</EquationSource> </InlineEquation> and obtain the torsion codes of them.</p>

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Skew constacyclic codes of length \(p^s\) over \(\mathbb {F}_{p^m}+u\mathbb {F}_{p^m}+u^2\mathbb {F}_{p^m}\)

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Roghaye Mohammadi Hesari,
  • Karim Samei

摘要

In this paper, we characterize the skew constacyclic codes of length \( p^s \) over \( R_3= \mathbb {F}_{p^m}+u\mathbb {F}_{p^m}+{u^2}\mathbb {F}_{p^m}\) for special automorphisms, where p is a prime, m is a positive integer, \( \mathbb {F}_{p^m} \) is a finite field of cardinality \( p^m\) and \( u^3=0. \) First, we classify all skew constacyclic codes of length \( p^s \) over \( R_3\) and obtain the torsion codes of them.