Harmonic Tutte polynomials of matroids II

Thomas Britz, Himadri Shekhar Chakraborty*, Reina Ishikawa, Tsuyoshi Miezaki, Hopein Christofen Tang

*この研究の対応する著者

研究成果: Article査読

抄録

In this work, we introduce the harmonic generalization of the m-tuple weight enumerators of codes over finite Frobenius rings. A harmonic version of the MacWilliams-type identity for m-tuple weight enumerators of codes over finite Frobenius ring is also given. Moreover, we define the demi-matroid analogue of well-known polynomials from matroid theory, namely Tutte polynomials and coboundary polynomials, and associate them with a harmonic function. We also prove the Greene-type identity relating these polynomials to the harmonic m-tuple weight enumerators of codes over finite Frobenius rings. As an application of this Greene-type identity, we provide a simple combinatorial proof of the MacWilliams-type identity for harmonic m-tuple weight enumerators over finite Frobenius rings. Finally, we provide the structure of the relative invariant spaces containing the harmonic m-tuple weight enumerators of self-dual codes over finite fields.

本文言語English
ページ(範囲)1279-1297
ページ数19
ジャーナルDesigns, Codes, and Cryptography
92
5
DOI
出版ステータスPublished - 2024 5月

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 応用数学
  • 離散数学と組合せ数学
  • コンピュータ サイエンスの応用

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