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On the second weight of generalized Reed-Muller codes

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An Erratum to this article was published on 24 April 2014

Abstract

Not much is known about the weight distribution of the generalized Reed-Muller code RM q (s,m) when q > 2, s > 2 and m ≥ 2. Even the second weight is only known for values of s being smaller than or equal to q/2. In this paper we establish the second weight for values of s being smaller than q. For s greater than (m – 1)(q – 1) we then find the first s + 1 – (m – 1)(q–1) weights. For the case m = 2 the second weight is now known for all values of s. The results are derived mainly by using Gröbner basis theoretical methods.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark

    Olav Geil

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  1. Olav Geil
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Correspondence to Olav Geil.

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Communicated by G. McGuire.

An erratum to this article is available at http://dx.doi.org/10.1007/s10623-014-9966-0.

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Geil, O. On the second weight of generalized Reed-Muller codes. Des. Codes Cryptogr. 48, 323–330 (2008). https://doi.org/10.1007/s10623-008-9211-9

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  • DOI: https://doi.org/10.1007/s10623-008-9211-9

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