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<p>In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {F}=\mathbb {F}_q\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">F</mi> <mo>=</mo> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>. We obtain the generator matrices and generator polynomials of these codes and their duals. We also investigate when such codes are self-dual. </p>

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One-Sided Repeated-Root Two-Dimensional Cyclic and Constacyclic Codes

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Marziyeh Beygi Khormaei,
  • Ashkan Nikseresht,
  • Shohreh Namazi

摘要

In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field \(\mathbb {F}=\mathbb {F}_q\) F = F q . We obtain the generator matrices and generator polynomials of these codes and their duals. We also investigate when such codes are self-dual.