On the kernel of Z2s-linear hadamard codes

Cristina Fernández-Córdoba, Carlos Vela*, Mercè Villanueva

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


The Z2s-additive codes are subgroups of Z2s n, and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s -linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s -additive code. For s=2, the kernel of Z4 -linear Hadamard codes can be used for their complete classification. In this paper, the kernel of Z2s -linear Hadamard codes is given for s > 2. However, unlike for s=2, we show that the dimension of the kernel just allows a partial classification of these Hadamard codes.


  • Classification
  • Gray map
  • Hadamard code
  • Kernel
  • Z-additive code
  • Z-linear code


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