On the secrecy gain of $\ell$-modular lattices
نویسندگان
چکیده
We show that for every ` > 1, there is a counterexample to the `-modular secrecy function conjecture by Oggier, Solé and Belfiore. These counterexamples all satisfy the modified conjecture by Ernvall-Hytönen and Sethuraman. Furthermore, we provide a method to prove or disprove the modified conjecture for any given `-modular lattice rationally equivalent to a suitable amount of copies of Z⊕ √ `Z with ` ∈ {3, 5, 7, 11, 23}. We also provide a variant of the method for strongly `-modular lattices when ` ∈ {6, 14, 15}.
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عنوان ژورنال:
- CoRR
دوره abs/1708.09239 شماره
صفحات -
تاریخ انتشار 2017