Harmonic higher and extended weight enumerators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915340921864192 |
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| author | Britz, Thomas Chakraborty, Himadri Shekhar Miezaki, Tsuyoshi |
| author_facet | Britz, Thomas Chakraborty, Himadri Shekhar Miezaki, Tsuyoshi |
| contents | In this paper, we present the harmonic generalizations of well-known polynomials of codes over finite fields, namely the higher weight enumerators and the extended weight enumerators, and we derive the correspondences between these weight enumerators. Moreover, we present the harmonic generalization of Greene's Theorem for the higher (resp. extended) weight enumerators. As an application of this Greene's-type theorem, we provide the MacWilliams-type identity for harmonic higher weight enumerators of codes over finite fields. Finally, we use this new identity to give a new proof of the Assmus-Mattson Theorem for subcode supports of linear codes over finite fields using harmonic higher weight enumerators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16948 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harmonic higher and extended weight enumerators Britz, Thomas Chakraborty, Himadri Shekhar Miezaki, Tsuyoshi Combinatorics Group Theory Number Theory In this paper, we present the harmonic generalizations of well-known polynomials of codes over finite fields, namely the higher weight enumerators and the extended weight enumerators, and we derive the correspondences between these weight enumerators. Moreover, we present the harmonic generalization of Greene's Theorem for the higher (resp. extended) weight enumerators. As an application of this Greene's-type theorem, we provide the MacWilliams-type identity for harmonic higher weight enumerators of codes over finite fields. Finally, we use this new identity to give a new proof of the Assmus-Mattson Theorem for subcode supports of linear codes over finite fields using harmonic higher weight enumerators. |
| title | Harmonic higher and extended weight enumerators |
| topic | Combinatorics Group Theory Number Theory |
| url | https://arxiv.org/abs/2405.16948 |