Technical Report CS0787

TR#:CS0787
Class:CS
Title: SPECTRAL-NULL CODES AND NULL SPACES OF HADAMARD SUBMATRICES.
Authors: R.M. Roth
PDFCS0787.pdf
Abstract:

Codes \mbox{\boldmathC}(m,r) of length 2^m over \{1,-1\} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of \mbox{\boldmathC}(m,r) all have an rth order spectral null at zero frequency. Establishing the connection between \mbox{\boldmathC}(m,r) and the parity-check matrix of Reed-Muller codes, the minimum distance of \mbox{\boldmathC}(m,r) is obtained along with upper bounds on the redundancy of \mbox{\boldmathC}(m,r). An efficient algorithm is presented for encoding unconstrained binary sequences into \mbox{\boldmathC}(m,r).

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