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Configuration matrices of group codes

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1 Author(s)

Properties of configuration matrices of group codes for the Gaussian channel are considered. It is shown that the configuration matrix of a code generated by a real-irreducible representation is a scalar multiple of an idempotent matrix. A spectral resolution of the configuration matrix of a code generated by an arbitrary real representation is given, and all of its eigenvalues are determined. A relatively simple criterion to determine when the group code spans the space is derived.

Published in:

IEEE Transactions on Information Theory  (Volume:20 ,  Issue: 1 )