On components of the Kerdock codes and the dual of the BCH code C1,3

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Abstract

In the paper we investigate the structure of i-components of two classes of codes: the Kerdock codes and the duals of the linear uniformly packed codes with parameters of the primitive double-error-correcting BCH code. We prove that for any admissible length the punctured Kerdock code consists of two i-components and the duals of the linear uniformly packed codes with parameters of the primitive double-error-correcting BCH code is an i-component for any i. We give an alternative proof for the fact presented by De Caen and van Dam in 1999 that the restrictions of the Hamming scheme to the doubly shortened Kerdock codes are association schemes.

Original languageEnglish
Article number111668
Number of pages7
JournalDiscrete Mathematics
Volume343
Issue number2
DOIs
Publication statusPublished - Feb 2020

Keywords

  • Association scheme
  • BCH code
  • i-component
  • Kerdock code
  • t–design
  • Uniformly packed code
  • t-design
  • ASSOCIATION SCHEMES

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