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The Gray Map on GR(p 2, n) and Repeated-Root Cyclic Codes

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Finite Fields and Applications (Fq 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

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Abstract

It is shown that the Gray map on \(\mathbb{Z}^n_{p^2}\), where p is a prime and n a positive integer, yields the same result as an appropriate extension of the well-known “(u|u+v)-construction”. It is also shown that, up to a permutation, which is a generalization of Nechaev’s permutation, the Gray image of certain \(\mathbb{Z}_{p^2}\)-codes of length n constructed from \(\mathbb{F}_p\)-cyclic codes of length n are \(\mathbb{F}_p\)-cyclic codes of length pn with multiple roots. These results generalize some of those appearing in [21]. Examples are given in order to illustrate the ideas.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma Metropolitana-I, 09340, México, D.F., Mexico

    Horacio Tapia-Recillas

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  1. Horacio Tapia-Recillas
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Editors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, 16802, PA, USA

    Gary L. Mullen

  2. University Paul Sabatier, AAECC/IRIT, 118 route de Narbonne, 31300, Toulouse cedex, France

    Alain Poli

  3. Sabancı University - FENS, Orhanli - Tuzla, 34956, Istanbul, Turkey

    Henning Stichtenoth

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Tapia-Recillas, H. (2004). The Gray Map on GR(p 2, n) and Repeated-Root Cyclic Codes. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_15

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

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