Abstract
In this paper we extend results on Kneser–Hecke-operators for codes over finite fields, to the setting of codes over finite chain rings. In particular, we consider chain rings of the form \(\mathbb{Z}/p^{2}\mathbb{Z}\) for p prime. On the set of self-dual codes of length N, we define a linear operator, T, and characterize its associated eigenspaces.
This work was started at the WIN3 workshop at the Banff International Research Station in Banff, Canada. The authors wish to thank the organizers for their tremendous efforts, and for providing the opportunity to begin this collaboration. They also wish to thank the referees for their helpful comments and suggestions.
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Feaver, A., Haensch, A., Liu, J., Nebe, G. (2016). Kneser–Hecke-Operators for Codes over Finite Chain Rings. In: Eischen, E., Long, L., Pries, R., Stange, K. (eds) Directions in Number Theory. Association for Women in Mathematics Series, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-30976-7_8
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DOI: https://doi.org/10.1007/978-3-319-30976-7_8
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