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arXiv · 2608.09040

Universally optimal (wiretap) codes

Madhura Pathegama·Alexander Barg
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Abstract

Universally optimal (UO) codes were introduced by H. Cohn and A. Kumar in 2007 and later extended to the discrete setting by Cohn and Y. Zhao. They minimize the ``energy'' among all codes of the same size for a certain class of potential functions. So far only a small number of specific functionals have been linked to information theory problems. We add one more, showing that UO codes optimize $\alpha$-mutual information for $\alpha=2$ in the context of wiretap channels with a noiseless main channel. This implies that UO codes are optimal for transmission over this type of wiretap channels.

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Madhura Pathegama, Alexander Barg. 2026-08-10. Universally optimal (wiretap) codes. https://arxiv.org/abs/2608.09040

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