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<p>Recently, double Toeplitz codes and four Toeplitz (FT) codes, which are generalizations of double circulant codes and four circulant codes respectively, have been introduced for constructing linear complementary dual (LCD) codes and formally self-dual (FSD) as well as their combination, namely FSD LCD codes. This paper focuses on FT codes derived from tridiagonal and pentadiagonal Toeplitz matrices, and characterizes their LCD properties in term of eigenvalues.</p>

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Formally self-dual linear complementary dual codes associated with Toeplitz matrices

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Yan Liu,
  • Xiaoyu Yu,
  • Shanshan Liu,
  • Juan Wang

摘要

Recently, double Toeplitz codes and four Toeplitz (FT) codes, which are generalizations of double circulant codes and four circulant codes respectively, have been introduced for constructing linear complementary dual (LCD) codes and formally self-dual (FSD) as well as their combination, namely FSD LCD codes. This paper focuses on FT codes derived from tridiagonal and pentadiagonal Toeplitz matrices, and characterizes their LCD properties in term of eigenvalues.