Hadamard codes of length 2ts (s Odd). rank and kernel

Authors:
Kevin T. Phelps;Josep Rifà;Mercè Villanueva
Affiliations:
Dept. of Mathematics and Statistics, Auburn University, Auburn, Al;Dept. of Information and Communications Engineering, Universitat Autònoma de Barcelona, Spain;Dept. of Information and Communications Engineering, Universitat Autònoma de Barcelona, Spain
Venue:
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2006

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Abstract

The rank, r, and the dimension of the kernel, k, for binary Hadamard codes of length 2twere studied in [12], constructing such codes for all possible pairs (r,k). Now, we will focus on Hadamard codes of length 2t· s, s1 odd. As long as there exists a Hadamard code of length 4s, constructions of Hadamard codes of length n=2t· s (t≥ 3) with any rank, r ∈ {4s+t–3,..., n/2}, and any possible dimension of the kernel, k∈ {1,...,t–1}, are given.