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<p>This paper aims to define linear Gray functions over the Frobenius non-chain ring <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(GF(2^d)[X,Y,Z]/\langle X^2, Y^2, YZ, XZ, Z^2-XY\rangle \)</EquationSource> </InlineEquation>. Some Gray functions map linear codes to codes consisting of 2<i>n</i> transpositions, while others map linear codes to codes with an automorphism consisting of n transpositions. Self-orthogonal constacyclic codes over rings whose maximal ideals have nilpotency index three are thoroughly described, where the length of the code is relatively prime to the characteristic of the residue field of the ring. Hence, these codes over our ring are determined, and their Gray images are discussed.</p>

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Gray functions and self-orthogonal codes on \(GF(2^d)[X,Y,Z]/\langle X^2, Y^2, YZ, XZ, Z^2-XY\rangle \)

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Cain Álvarez-García,
  • Carlos Alberto Castillo-Guillén,
  • Mohamed Badaoui,
  • Jaime Robles-García

摘要

This paper aims to define linear Gray functions over the Frobenius non-chain ring \(GF(2^d)[X,Y,Z]/\langle X^2, Y^2, YZ, XZ, Z^2-XY\rangle \) . Some Gray functions map linear codes to codes consisting of 2n transpositions, while others map linear codes to codes with an automorphism consisting of n transpositions. Self-orthogonal constacyclic codes over rings whose maximal ideals have nilpotency index three are thoroughly described, where the length of the code is relatively prime to the characteristic of the residue field of the ring. Hence, these codes over our ring are determined, and their Gray images are discussed.