Search for tag: "Coding Theory"

Ferrers diagram rank-metric codes were first studied in 2009 by Etzion and Silberstein, motivated by their application in network coding. Concretely, they arise from subspace codes entirely contained…

A one-weight code, or constant-weight code, is an error-correcting code in which all codewords share the same weight. In 1984, Bonisoli provided a classification of one-weight linear codes by…

Generalized Hamming Weights (GHW) have seen a big rise in popularity since Victor Wei described their many properties in 1991, linking them to code performance on the wire-tap channel of type 2.…

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In this talk, we investigate a particular family of graphs with large girth and look at their applications to low-density parity-check (LDPC) codes. Specifically, we study a family of Cayley…

As our technology advances, the need for b-symbol read channels that can handle messages with high-density data becomes crucial. The problem with conventional read channels is that they are more…

In my previous research, during my PhD and several years as a postdoc, I studied endomorphisms of the projective line. More specifically, I focused on rational functions that can be represented…

Planar functions are functions defined over finite fields of odd characteristics such that their (nonzero) derivatives are permutations. They have connections with various areas of mathematics with…

Code-based cryptography is an area of post-quantum cryptography. Several code-based candidates compete in the standardization process of the National Institute of Standards and Technology. A common…

The MinRank Problem is the computational problem of finding a low rank linear combination of a set of matrices. There are several cryptographic attacks that can be reduced to MinRank. During this…

We investigate the properties of a family of polytopes that naturally arise in connection with a problem in distributed data storage, namely service rate region polytopes. We make use of polytope…

In this talk we study the BIKE cryptosystem. We will introduce a lattice over a polynomial ring which we construct from the public key. The private key is a vector in this lattice with special…

We provide a concise introduction to CSS and CSS-T codes from the perspective of classical coding theory. We demonstrate that pairs of linear codes that yield a CSS code with good correction…

There exist Singleton-like upper bounds for the column distances of convolutional codes, which can be reached if the underlying finite field is sufficiently large. However, it is not known which…

Jens Kopp's masters thesis defense.