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One-weight codes in some classes of group rings

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Abstract

Let \({\mathbb {F}}_q\) be a finite field with q elements and G be a finite abelian group. In this work we gave conditions to ensure that a code in \({\mathbb {F}}_qG\) is a one-weight code in the case when G is a cyclic group with n elements, such that \({\text {gcd}}(n,q) = 1\), and also when G is an abelian group.

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Acknowledgements

The authors are very grateful to Prof. César Polcino Milies for useful conversations while this work was done. The first author was partially supported by FAPESP Proc. 2015/09162-9. The second author was partially supported by CAPES-PROEX and CNPq Proc. 163425/2013-2. The authors are very grateful to Thiago Augusto S. Dourado for his help in the text processing.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de São Paulo, Rua do Matão, 1010, 05508-090, São Paulo SP, Brazil

    Raul Antonio Ferraz

  2. Universidade Tecnológica Federal do Paraná, Avenida Professora Laura Pacheco Bastos, 800, 85053-510, Guarapuava PR, Brazil

    Ruth Nascimento Ferreira

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  1. Raul Antonio Ferraz
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  2. Ruth Nascimento Ferreira
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Correspondence to Raul Antonio Ferraz.

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Ferraz, R.A., Ferreira, R.N. One-weight codes in some classes of group rings. AAECC 32, 299–309 (2021). https://doi.org/10.1007/s00200-020-00471-7

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