Harmonic Tutte polynomials of matroids II

被引：0
作者：
Thomas Britz
Himadri Shekhar Chakraborty
Reina Ishikawa
Tsuyoshi Miezaki
Hopein Christofen Tang
机构：
[1] University of New South Wales,School of Mathematics and Statistics
[2] Shahjalal University of Science and Technology,Department of Mathematics
[3] Waseda University,Graduate School of Science and Engineering
[4] Waseda University,Faculty of Science and Engineering
来源：
Designs, Codes and Cryptography | 2024年 / 92卷
关键词：
Tutte polynomials; Coboundary polynomials; Weight enumerators; Demi-matroids; Harmonic functions; Primary 11T71; Secondary 94B05; 11F11;
D O I：
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中图分类号：
学科分类号：
摘要：
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.
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页码：1279 / 1297
页数：18
相关论文
共 34 条
[1]  
Bachoc C(1999)On harmonic weight enumerators of binary codes Des. Codes Cryptogr. 18 11-28
[2]  
Berlekamp ER(1972)Gleason’s theorem on self-dual codes IEEE Trans. Inform. Theory IT–18 409-414
[3]  
MacWilliams FJ(1997)The Magma algebra system. I. The user language J. Symb. Comput. 24 235-265
[4]  
Sloane NJA(2012)Wei-type duality theorems for matroids Des. Codes Cryptogr. 62 331-341
[5]  
Bosma W(2008)A MacWilliams-type identity for matroids Discret. Math. 308 4551-4559
[6]  
Cannon J(2015)Demi-matroids from codes over finite Frobenius rings Des. Codes Cryptogr. 75 97-107
[7]  
Playoust C(2023)Harmonic Tutte polynomials of matroids Des. Codes Cryptogr. 91 2223-2236
[8]  
Britz T(1969)The Tutte polynomial Aequ. Math. 3 211-229
[9]  
Johnsen T(1978)Hahn polynomials, discrete harmonics, and SIAM J. Appl. Math. 34 157-166
[10]  
Mayhew D(1976)-designs Appl. Math. 55 119-128
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