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2- and 3-modular lattice wiretap codes in small dimensions. (English) Zbl 1343.94098
Summary: A recent line of work on lattice codes for Gaussian wiretap channels introduced a new lattice invariant called secrecy gain as a code design criterion which captures the confusion that lattice coding produces at an eavesdropper. Following up the study of unimodular lattice wiretap codes [F. Lin and F. Oggier, IEEE Trans. Inf. Theory 59, No. 6, 3295–3303 (2013; doi:10.1109/TIT.2013.2246814)], this paper investigates 2- and 3-modular lattices which can be constructed from linear codes and compares them with unimodular lattices. Most even 2- and 3-modular lattices are found to have better performance (that is, a higher secrecy gain) than the best unimodular lattices in dimension \(n\), \(2\leq n\leq 23\). Odd 2-modular lattices are considered, too, and three lattices are found to outperform the best unimodular lattices.

94B25 Combinatorial codes
Magma; Mathematica
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