On a conjecture by Belfiore and Solé on some lattices
نویسنده
چکیده
The point of this note is to prove that the secrecy function attains its maximum at y = 1 on all known extremal even unimodular lattices. This is a special case of a conjecture by Belfiore and Solé. Further, we will give a very simple method to verify or disprove the conjecture on any given unimodular lattice.
منابع مشابه
Some results related to the conjecture by Belfiore and Solé
In the first part of the paper, we consider the relation between kissing number and the secrecy gain. We show that on an n = 24m+8k-dimensional even unimodular lattice, if the shortest vector length is ≥ 2m, then as the number of vectors of length 2m decreases, the secrecy gain increases. We will also prove a similar result on general unimodular lattices. We will also consider the situations wi...
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ورودعنوان ژورنال:
- IEEE Trans. Information Theory
دوره 58 شماره
صفحات -
تاریخ انتشار 2012