Z <inf>2</inf> Z <inf>4</inf> -Additive Cyclic Codes: Kernel and Rank

Joaquim Borges, Steven T. Dougherty, Cristina Fernández-Córdoba, Roger Ten-Valls

Research output: Contribution to journalArticleResearch

Abstract

© 2018 IEEE. A Z 2 Z 4 -additive code C ∪ Zα 2 × Zβ 4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 coordinates and the set of Z 4 coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. Let φ (C) be the binary Gray map image of C. We study the rank and the dimension of the kernel of a Z 2 Z 4 -additive cyclic code C, that is, the dimensions of the binary linear codes φ(C) and ker(φ (C)). We give upper and lower bounds for these parameters. It is known that the codes φ (C) and ker(φ (C)) are binary images of Z 2 Z 4 -additive codes that we denote by R(C) and K(C), respectively. Moreover, we show that R(C) and K(C) are also cyclic and determine the generator polynomials of these codes in terms of the generator polynomials of the code C.
Original languageEnglish
Article number8469015
Pages (from-to)2119-2127
JournalIEEE Transactions on Information Theory
Volume65
DOIs
Publication statusPublished - 1 Apr 2019

Keywords

  • Gray map
  • kernel
  • rank
  • Z Z -additive cyclic codes 2 4

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