Hadamard full propelinear codes of type Q; rank and kernel

J. Rifà, Emilio Suárez Canedo

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

© 2017, Springer Science+Business Media, LLC. Hadamard full propelinear codes (HFP -codes) are introduced and their equivalence with Hadamard groups is proven; on the other hand, the equivalence of Hadamard groups, relative (4n, 2, 4n, 2n)-difference sets in a group, and cocyclic Hadamard matrices, is already known. We compute the available values for the rank and dimension of the kernel of HFP -codes of type Q and we show that the dimension of the kernel is always 1 or 2. We also show that when the dimension of the kernel is 2 then the dimension of the kernel of the transposed code is 1 (so, both codes are not equivalent). Finally, we give a construction method such that from an HFP -code of length 4n, dimension of the kernel k= 2 , and maximum rank r= 2 n, we obtain an HFP -code of double length 8n, dimension of the kernel k= 2 , and maximum rank r= 4 n.
Original languageEnglish
Pages (from-to)1905-1921
JournalDesigns, Codes, and Cryptography
Volume86
Issue number9
DOIs
Publication statusPublished - 1 Sep 2018

Keywords

  • Cocyclic Hadamard matrix
  • Hadamard code
  • Hadamard group
  • Kernel
  • Propelinear code
  • Rank
  • Relative difference set

Fingerprint Dive into the research topics of 'Hadamard full propelinear codes of type Q; rank and kernel'. Together they form a unique fingerprint.

Cite this