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We review the zeta-function representation of codewords allowed by aparity-check code based on a bipartite graph, and then investigate the effectof disorder on the effective distribution of codewords. The randomness (ordisorder) is implemented by sampling the graph from an ensemble of randomgraphs, and computing the average zeta function of the ensemble. In the limitof arbitrarily large size for the vertex set of the graph, we find anexponential decay of the likelihood for nontrivial codewords corresponding tograph cycles. This result provides a quantitative estimate of the effect ofrandomization in cybersecurity applications.

Effective distribution of codewords for Low Density Parity Check Cycle codes in the presence of disorder