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The Weight Distribution for an Extended Family of Reducible Cyclic Codes

  • Gerardo VegaEmail author
  • Jesús E. Cuén-Ramos
Conference paper
  • 679 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10194)

Abstract

The purpose of this work is to present new advances on the weight distribution of the duals of some cyclic codes with two zeros. More specifically, our contribution improves the sufficient numerical conditions that determine the weight distribution for the class of reducible cyclic codes that were studied in [19] and in [17]. Furthermore, as will be shown later, a conclusion here will be that thanks to these previous works and the present contribution, we can determine the weight distribution for an extended family of reducible cyclic codes. More specifically, we are going to determine the weight distribution for all the elements of an extended family of reducible cyclic codes that fully covers one of the open cases suggested in [20]. In addition, as will be seen further on, through our results we obtain an alternative description for one of the families of cross-correlation functions studied in [8].

Keywords

Weight distribution Reducible cyclic codes Gaussian periods Cross-correlation functions 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dirección General de Cómputo y de Tecnologías de Información y Comunicación, Universidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico
  2. 2.Posgrado en Ciencias Matemáticas, Universidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico

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