Ranks and kernels of codes from generalized Hadamard matrices

Steven T. Dougherty, Josep Rifà, Mercè Villanueva

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


© 2015 IEEE. The ranks and kernels of generalized Hadamard matrices are studied. It is proved that any generalized Hadamard matrix H(q,λ) over Fq, q > 3, or q = 3 and gcd(3, λ) = 1, generates a self-orthogonal code. This result puts a natural upper bound on the rank of the generalized Hadamard matrices. Lower and upper bounds are given for the dimension of the kernel of the corresponding generalized Hadamard codes. For specific ranks and dimensions of the kernel within these bounds, generalized Hadamard codes are constructed.
Original languageEnglish
Article number7362191
Pages (from-to)687-694
JournalIEEE Transactions on Information Theory
Publication statusPublished - 1 Feb 2016


  • Generalized Hadamard code
  • Generalized Hadamard matrix
  • Kernel
  • Nonlinear code
  • Rank
  • Self-orthogonal code

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