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arXiv · 0908.1966

Spectral Graph Analysis of Quasi-Cyclic Codes

Roxana Smarandache·Mark F. Flanagan
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Abstract

In this paper we analyze the bound on the additive white Gaussian noise channel (AWGNC) pseudo-weight of a (c,d)-regular linear block code based on the two largest eigenvalues of H^T H. In particular, we analyze (c,d)-regular quasi-cyclic (QC) codes of length rL described by J x L block parity-check matrices with circulant block entries of size r x r. We proceed by showing how the problem of computing the eigenvalues of the rL x rL matrix H^T H can be reduced to the problem of computing eigenvalues for r matrices of size L x L. We also give a necessary condition for the bound to be attained for a circulant matrix H and show a few classes of cyclic codes satisfying this criterion.

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Roxana Smarandache, Mark F. Flanagan. 2009-08-16. Spectral Graph Analysis of Quasi-Cyclic Codes. https://arxiv.org/abs/0908.1966

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