Can I read Secrecy Gain of Formally Unimodular Lattices from Codes over the Integers Modulo 4 on EtoBox?

Secrecy Gain of Formally Unimodular Lattices from Codes over the Integers Modulo 4 by Bollauf, Maiara F.; Lin, Hsuan-Yin; Ytrehus, Øyvind is a scholarly article available to read on EtoBox.

What is Secrecy Gain of Formally Unimodular Lattices from Codes over the Integers Modulo 4 about?

Recently, a design criterion depending on a lattice's volume and theta series, called the secrecy gain, was proposed to quantify the secrecy-goodness of the applied lattice code for the Gaussian wiretap channel. To address the secrecy gain of Construction $\text{A}_4$ lattices from formally self-dual $\mathbb{Z}_4$-linear codes, i.e., codes for which the symmetrized weight enumerator (swe) coincides with the swe of its dual, we present new constructions of $\mathbb{Z}_4$-linear codes which are formally self-dual with respect to the swe. For even lengths, formally self-dual $\mathbb{Z}_4$-linear codes are constructed from nested binary codes and double circulant matrices. For odd lengths, a novel construction called odd extension from double circulant codes is proposed. Moreover, the concepts of Type I/II formally self-dual codes/unimodular lattices are introduced. Next, we derive the theta series of the formally unimodular lattices obtained by Construction $\text{A}_4$ from formally self-dual $\mathbb{Z}_4$-linear codes and describe a universal approach to determine their secrecy gains. The secrecy gain of Construction $\text{A}_4$ formally unimodular lattices obtained from formall

Author

Bollauf, Maiara F.; Lin, Hsuan-Yin; Ytrehus, Øyvind

Published

2023

Language

EN