Patrick Solé

Lattice Codes for the Wiretap Gaussian Channel: Construction and Analysis

We consider the Gaussian wiretap channel, where two legitimate players Alice and Bob communicate over an additive white Gaussian noise (AWGN) channel, while Eve is eavesdropping, also through an AWGN channel. We propose a coding strategy based on lattice coset encoding. We define the secrecy gain as a design criterion for wiretap lattice codes, expressed in terms of the lattice theta series, which characterizes Eve’s confusion as a function of the channel parameters. The secrecy gain is studied for even unimodular lattices, and an asymptotic analysis shows that it grows exponentially in the dimension of the lattice. Examples of wiretap lattice codes are given.

Quasi-cyclic complementary dual codes

Linear complementary dual codes are linear codes that intersect with their dual trivially. Quasi-cyclic codes that are complementary dual are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian linear complementary dual codes are introduced to that end and their cyclic subclass is characterized. Constructions of quasi-cyclic complementary dual codes from codes over larger alphabets are given.

Optimal Two-Weight Codes From Trace Codes Over 𝔽 2 +u𝔽 2 .

We construct an infinite family of two-Lee-weight codes over the ring F2 t uF2. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. By Gray mapping, we obtain an infinite family of abelian binary two-weight codes. They are shown to be optimal by application of the Griesmer bound. An application to secret sharing schemes is given.

Two New Families of Two-Weight Codes

We construct two new infinite families of trace codes of dimension <inline-formula> <tex-math notation=LaTeX>

Xing---Ling codes, duals of their subcodes, and good asymmetric quantum codes

2m

Towards the classification of self-dual bent functions in eight variables

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Structure and performance of generalized quasi-cyclic codes

mathbb {F}_{p}+umathbb {F}_{p}

On the lifted Zetterberg code

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2- and 3-Modular lattice wiretap codes in small dimensions

u^{2}=u

On self-dual double circulant codes

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