TY - JOUR
T1 - Ranks and kernels of codes from generalized Hadamard matrices
AU - Dougherty, Steven T.
AU - Rifà, Josep
AU - Villanueva, Mercè
PY - 2016/2/1
Y1 - 2016/2/1
N2 - © 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.
AB - © 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.
KW - Generalized Hadamard code
KW - Generalized Hadamard matrix
KW - Kernel
KW - Nonlinear code
KW - Rank
KW - Self-orthogonal code
U2 - 10.1109/TIT.2015.2509061
DO - 10.1109/TIT.2015.2509061
M3 - Article
SN - 0018-9448
VL - 62
SP - 687
EP - 694
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
M1 - 7362191
ER -