Ranks and kernels of codes from generalized Hadamard matrices

Steven T. Dougherty, Josep Rifà, Mercè Villanueva

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Resum

© 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.
Idioma originalAnglès
Número d’article7362191
Pàgines (de-a)687-694
RevistaIEEE Transactions on Information Theory
Volum62
DOIs
Estat de la publicacióPublicada - 1 de febr. 2016

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