On hadamard full propelinear codes with associated group C2t × C2

Ivan Bailera*, Joaquim Borges, Josep Rifà

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16.

Original languageEnglish
Pages (from-to)35-54
Number of pages20
JournalAdvances in Mathematics of Communications
Volume15
Issue number1
DOIs
Publication statusPublished - Feb 2021

Keywords

  • Hadamard full propelinear codes
  • Hadamard matrices
  • Kernel
  • Rank

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