Harmonic Tutte polynomials of matroids II
Copyright policy )Harmonic Tutte polynomials of matroids II
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.
23 pages
- Waseda University Japan
- Shahjalal University of Science and Technology Bangladesh
- UNSW Sydney Australia
FOS: Computer and information sciences, anzsrc-for: 0804 Data Format, Computer Science - Information Theory, Primary 11T71, Secondary 94B05, 11F11, Group Theory (math.GR), anzsrc-for: 0101 Pure Mathematics, anzsrc-for: 4904 Pure Mathematics, 510, anzsrc-for: 40 Engineering, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), anzsrc-for: 0802 Computation Theory and Mathematics, anzsrc-for: 46 Information and computing sciences, Mathematics - Number Theory, Information Theory (cs.IT), 4901 Applied Mathematics, 4904 Pure Mathematics, 004, anzsrc-for: 49 Mathematical Sciences, 49 Mathematical Sciences, anzsrc-for: 4901 Applied Mathematics, Combinatorics (math.CO), Mathematics - Group Theory
FOS: Computer and information sciences, anzsrc-for: 0804 Data Format, Computer Science - Information Theory, Primary 11T71, Secondary 94B05, 11F11, Group Theory (math.GR), anzsrc-for: 0101 Pure Mathematics, anzsrc-for: 4904 Pure Mathematics, 510, anzsrc-for: 40 Engineering, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), anzsrc-for: 0802 Computation Theory and Mathematics, anzsrc-for: 46 Information and computing sciences, Mathematics - Number Theory, Information Theory (cs.IT), 4901 Applied Mathematics, 4904 Pure Mathematics, 004, anzsrc-for: 49 Mathematical Sciences, 49 Mathematical Sciences, anzsrc-for: 4901 Applied Mathematics, Combinatorics (math.CO), Mathematics - Group Theory
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