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On the evaluation codes given by simple \(\delta \)-sequences

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Abstract

Plane valuations at infinity are classified in five types. Valuations in one of them determine weight functions which take values on semigroups of \({\mathbb Z}^2\). These semigroups are generated by \(\delta \)-sequences in \({\mathbb Z}^2\). We introduce simple \(\delta \)-sequences in \({\mathbb Z}^2\) and study the evaluation codes of maximal length that they define. These codes are geometric and come from order domains. We give a bound on their minimum distance which improves the Andersen–Geil one. We also give coset bounds for the involved codes.

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Acknowledgments

The authors would like to thank the reviewers for their valuable comments and effort to improve the manuscript.

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Author notes

  1. C. Galindo

    Present address: Departamento de Matemáticas & Instituto Universitario de Matemáticas y Aplicaciones de Castellón (IMAC), Universitat Jaume I, Campus de Riu Sec, 12071, Castellón, Spain

Authors and Affiliations

  1. Departamento de Ciencia de la Computación, Facultad de Matemática y Computación, Universidad de Oriente, Santiago de Cuba, Cuba

    R. Pérez-Casales

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  1. C. Galindo
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Correspondence to C. Galindo.

Additional information

This study was supported by Spain Ministry of Economy MTM2012-36917-C03-03 and by Universitat Jaume I P1-1B2012-04.

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Galindo, C., Pérez-Casales, R. On the evaluation codes given by simple \(\delta \)-sequences. AAECC 27, 59–90 (2016). https://doi.org/10.1007/s00200-015-0271-6

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