10 papers · 1 filter
Graphical Analysis of Lifted Product Code Constructions
Ragnar Freij-Hollanti, Kirsten D. Morris, Patricija Šapokaitė
Lifted product codes are an important family of quantum low-density parity-check (QLDPC) codes, as they were the first QLDPC code family shown to be asymptotically good. Understand…
A -Polymatroid Framework for Information Leakage in Secure Linear Network Coding
Eimear Byrne, Johan Vester Dinesen, Ragnar Freij-Hollanti +1
We study information leakage in secure linear network coding schemes based on nested rank-metric codes. We show that the amount of information leaked to an adversary that observes…
The Star Product of Uniformly Random Codes
Johan Vester Dinesen, Ragnar Freij-Hollanti, Camilla Hollanti +2
We consider the problem of determining the expected dimension of the star product of two uniformly random linear codes that are not necessarily of the same dimension. We use a corr…
Secret Sharing in the Rank Metric
Johan Vester Dinesen, Eimear Byrne, Ragnar Freij-Hollanti +1
The connection between secret sharing and matroid theory is well established. In this paper, we generalize the concepts of secret sharing and matroid ports to -polymatroids. Spe…
Private Information Retrieval from Colluding and Byzantine Servers with Binary Reed-Muller Codes
Perttu Saarela, Matteo Allaix, Ragnar Freij-Hollanti +1
In this work, a flexible and robust private information retrieval (PIR) scheme based on binary non-maximum distance separable (non-MDS) codes is considered. This combines previous…
Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power
Julian Renner, Sven Puchinger, Antonia Wachter-Zeh +2
We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring , where is a prime and is a positive integer. LRPC…