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$\mathbb F_p$-codes, theta functions and the Hamming weight MacWilliams identity

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  • Hirzebruch and van der Geer attached theta functions to self-orthogonal, $C\subseteq C^{\bot}$, linear codes $C\subseteq\mathbb F_p^n$, for $p$ an odd prime, and related them to the Lee weight enumerator for the code [5, Ch. 5]. Choie and Jeong extended this result to Jacobi theta functions and provided an analytic proof of the Lee weight MacWilliams Identity for such $C$ [3]. We provide an analytic proof of the Hamming weight MacWilliams Identity for linear codes $C\subseteq\mathbb F_p^n$, generalizing the seminal result for binary codes $C\subseteq\mathbb F_2^n$ [2].
    Mathematics Subject Classification: Primary: 32N10, 11H71; Secondary: 11R04.


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