Abstract
We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids. We also prove a MacWilliams-type identity for Hamming support enumerators of linear codes over finite Frobenius rings. As a special case, these results give a combinatorial proof of the MacWilliams identity for Hamming weight enumerators of linear codes over finite Frobenius rings.
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Acknowledgments
Thomas Britz and Thomas Westerbäck were partly supported by a UNSW Faculty of Science Silverstar Grant.
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Communicated by D. Ghinelli.
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Britz, T., Shiromoto, K. & Westerbäck, T. Demi-matroids from codes over finite Frobenius rings. Des. Codes Cryptogr. 75, 97–107 (2015). https://doi.org/10.1007/s10623-013-9895-3
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DOI: https://doi.org/10.1007/s10623-013-9895-3