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- W4301166683 abstract "We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean space and weighted theta functions of Euclidean lattices. Namely, we use the finite-dimensional representation theory of sl_2 to derive a decomposition theorem for the spaces of discrete homogeneous polynomials in terms of the spaces of discrete harmonic polynomials, and prove a generalized MacWilliams identity for harmonic weight enumerators. We then present several applications of harmonic weight enumerators, corresponding to some uses of weighted theta functions: an equivalent characterization of t-designs, the Assmus-Mattson Theorem in the case of extremal Type II codes, and configuration results for extremal Type II codes of lengths 8, 24, 32, 48, 56, 72, and 96." @default.
- W4301166683 created "2022-10-04" @default.
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- W4301166683 date "2011-11-09" @default.
- W4301166683 modified "2023-09-25" @default.
- W4301166683 title "Weighted Generating Functions for Type II Lattices and Codes" @default.
- W4301166683 doi "https://doi.org/10.48550/arxiv.1111.2392" @default.
- W4301166683 hasPublicationYear "2011" @default.
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