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pro vyhledávání: '"Ytrehus, Oyvind"'
We propose an innovative approach to investigating the linearity of $\mathbb{Z}_{2^L}$-linear codes derived from $\mathbb{Z}_{2^L}$-additive codes using the generalized Gray map. To achieve this, we define two related binary codes: the associated and
Externí odkaz:
http://arxiv.org/abs/2309.12291
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 Constru
Externí odkaz:
http://arxiv.org/abs/2303.08083
This paper introduces the family of lattice-like packings, which generalizes lattices, consisting of packings possessing periodicity and geometric uniformity. The subfamily of formally unimodular (lattice-like) packings is further investigated. It ca
Externí odkaz:
http://arxiv.org/abs/2206.14171
Lattice coding for the Gaussian wiretap channel is considered, where the goal is to ensure reliable communication between two authorized parties while preventing an eavesdropper from learning the transmitted messages. Recently, a measure called secre
Externí odkaz:
http://arxiv.org/abs/2202.09236
We consider lattice coding for the Gaussian wiretap channel, where the challenge is to ensure reliable communication between two authorized parties while preventing an eavesdropper from learning the transmitted messages. Recently, a measure called th
Externí odkaz:
http://arxiv.org/abs/2111.01439
Autor:
Bollauf, Maiara F., Ytrehus, Øyvind
Motivated by applications in reliable and secure communication, we address the problem of tiling (or partitioning) a finite constellation in $\mathbb{Z}_{2^L}^n$ by subsets, in the case that the constellation does not possess an abelian group structu
Externí odkaz:
http://arxiv.org/abs/2105.04253
Systems of Boolean equations of low degree arise in a natural way when analyzing block ciphers. The cipher's round functions relate the secret key to auxiliary variables that are introduced by each successive round. In algebraic cryptanalysis, the at
Externí odkaz:
http://arxiv.org/abs/1710.08540
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is computed by u
Externí odkaz:
http://arxiv.org/abs/1709.01455
Autor:
Barbero, Ángela, Ytrehus, Øyvind
A systematic convolutional encoder of rate $(n-1)/n$ and maximum degree $D$ generates a code of free distance at most ${\cal D} = D+2$ and, at best, a column distance profile (CDP) of $[2,3,\ldots,{\cal D}]$. A code is \emph{Maximum Distance Separabl
Externí odkaz:
http://arxiv.org/abs/1705.10091
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