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Pàgina inicial > Articles > Articles publicats > Ranks and kernels of codes from generalized Hadamard matrices |
Data: | 2016 |
Resum: | 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. |
Ajuts: | Ministerio de Ciencia e Innovación TIN2013-40524-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-691 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Generalized Hadamard matrix ; Generalized Hadamard code ; Rank ; Kernel ; Nonlinear code ; Self-orthogonal code |
Publicat a: | IEEE transactions on information theory, Vol. 62 No. 2 (Feb. 2016) , p. 687-694, ISSN 0018-9448 |
Post-print 8 p, 1010.8 KB |