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Rank and kernel of binary Hadamard codes

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3 Author(s)
K. T. Phelps ; Dept. of Math. & Stat., Auburn Univ., AL, USA ; J. Rifa ; M. Villanueva

In this paper, the rank and the dimension of the kernel for (binary) Hadamard codes of length a power of two are studied. In general, it is well-known that the rank of a Hadamard code of length n=2t is a value in {t+1,...,n/2}. In the present paper, the range of possible values for the dimension of the kernel is computed and a construction of Hadamard codes of length n=2t for each one of these values is given. Lower and upper bounds for the rank and dimension of the kernel of a Hadamard code of length n=2t are also established. Finally, we construct Hadamard codes for all possible ranks and dimension of kernels between these bounds.

Published in:

IEEE Transactions on Information Theory  (Volume:51 ,  Issue: 11 )