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Codes over Σ2 m and Jacobi forms over the Quaternions

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

We introduce codes over the ring We relate self-dual codes over this ring to quaternionic unimodular lattices and to self-dual codes over via a gray map. We study a connection between the complete weight enumerators of codes over the quaternionic ring Σ2 m and Jacobi forms over the half-space of quaternions. This motivates us to construct an algebra homomorphism from a certain invariant polynomial ring, where the complete weight enumerators belong, to the ring of Jacobi forms over the quaternions. Higher genus modular forms over the quaternions are also constructed using joint weight enumerators of codes.

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Authors and Affiliations

  1. Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Korea

    YoungJu Choie

  2. Department of Mathematics, University of Scranton, Scranton, PA, 18510, USA

    Steven T. Dougherty2

Authors
  1. YoungJu Choie
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  2. Steven T. Dougherty2
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Correspondence to YoungJu Choie.

Additional information

This research was partially supported by KOSEF R01-2003-00011596-0

Some of the results of this paper were presented at the IEEE Information Theory Workshop, April, 2003

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Choie, Y., Dougherty2, S. Codes over Σ2 m and Jacobi forms over the Quaternions. AAECC 15, 129–147 (2004). https://doi.org/10.1007/s00200-004-0153-9

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  • DOI: https://doi.org/10.1007/s00200-004-0153-9

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