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Hadamard Full Propelinear Codes of type Q. Rank and Kernel [article]

J. Rifà, E. Suárez Canedo
2017 arXiv   pre-print
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.  ...  Hadamard full propelinear codes (HFP-codes) are introduced and their equivalence with Hadamard groups is proven (on the other hand, it is already known the equivalence of Hadamard groups with relative  ...  This work has been partially supported by the Spanish MICINN grants TIN2016-77918-P, MTM2015-69138-REDT and the Catalan AGAUR grant 2014SGR-691.  ... 
arXiv:1709.02465v2 fatcat:ay75pyokynd7tocqrxuj2bij6i

Hadamard full propelinear codes of type Q; rank and kernel

J. Rifà, Emilio Suárez Canedo
2017 Designs, Codes and Cryptography  
Acknowledgements Acknowledgements The authors are grateful to the anonymous referees for their helpful comments, which have improved the presentation of the results of this paper.  ...  This work has been partially supported by the Spanish MICINN Grants TIN2016-77918-P, MTM2015-69138-REDT and the Catalan AGAUR Grant 2014SGR-691.  ...  Rank and kernel of HFP-codes of type Q In this section we study the allowable values for the rank and for the dimension of the kernel of an HFP-code of type Q.  ... 
doi:10.1007/s10623-017-0429-2 fatcat:kj72v6m5pjhwbb7j62gcrwlh5m

Circulant Hadamard matrices as HFP-codes of type C_4n× C_2 [article]

Josep Rifà
2017 arXiv   pre-print
We compute the rank and dimension of the kernel of these kind of codes.  ...  We prove that a circulant Hadamard code of length 4n can always be seen as an HFP-code (Hadamard full propelinear code) of type C_4n× C_2, where C_2=〈 u〉 or the same, as a cocyclic Hadamard code.  ...  An Hadamard full propelinear code (HFP-code) is an Hadamard propelinear code C such that for every a ∈ C, a / ∈ {e, u} the permutation π a has not any fixed coordinate and π e = π u = I.  ... 
arXiv:1711.09373v1 fatcat:h44ehvyihvghpgrk2no7qdptfm

About some Hadamard full propelinear (2 t ,2,2)-codes. Rank and Kernel

I. Bailera, J. Borges, J. Rifà
2016 Electronic Notes in Discrete Mathematics  
A new subclass of Hadamard full propelinear codes is introduced in this article. We define the HFP(2t, 2, 2)-codes as codes with a group structure isomorphic to C 2t × C 2 2 .  ...  Concepts such as rank and dimension of the kernel are studied, and bounds for them are established. For t odd, r = 4t − 1 and k = 1.  ...  Rifà and Suárez [10] showed that the concept of Hadamard group is equivalent to Hadamard full propelinear codes.  ... 
doi:10.1016/j.endm.2016.09.055 fatcat:thzslnqcafhs3pbl4iecyrc6ou

Hadamard full propelinear codes with associated group C_2t× C_2; rank and kernel [article]

Ivan Bailera, Joaquim Borges, Josep Rifà
2019 arXiv   pre-print
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.  ...  We study the rank, the dimension of the kernel, and the structure of these codes.  ...  Table 1 : Rank and dimension of the kernel of Hadamard full propelinear codes with associated group C 2t ×C 2 .  ... 
arXiv:1808.08747v3 fatcat:7yc2exhqqzczdczb36zp4ugnye

On Hadamard full propelinear codes with associated group \begin{document}$ C_{2t}\times C_2 $\end{document}

Ivan Bailera, ,Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain, Joaquim Borges, Josep Rifà
2019 Advances in Mathematics of Communications  
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. 2010 Mathematics  ...  We study the rank, the dimension of the kernel, and the structure of these codes.  ...  Rank and dimension of the kernel of Hadamard full propelinear codes with associated group C 2t × C 2 .  ... 
doi:10.3934/amc.2020041 fatcat:iaracc6z7zbjjhtrlfo5exseoy

On the additive (/spl Zopf//sub 4/-linear and non-/spl Zopf//sub 4/-linear) Hadamard codes: rank and kernel

K.T. Phelps, J. Rifa, M. Villanueva
2006 IEEE Transactions on Information Theory  
All the possible non-isomorphic additive (Z4linear and non-Z4-linear) Hadamard codes are characterized and, for each one, the rank and the dimension of the kernel is computed. research interests include  ...  Josep Rifà was born in Manlleu, Catalonia (Spain) Barcelona and since 1992 he is a full professor and, at present, the Head of Information and Communications Engineering Department.  ...  Their comments have enabled us to improve the presentation of this paper.  ... 
doi:10.1109/tit.2005.860464 fatcat:zhxnoxlfpjbologt3vrgxtgfqu