Search for tag: "coding theory"

The sum-rank metric, which generalizes both the Hamming and rank metric, first appeared in 2005 in the context of space-time codes and later in 2010 for multi-shot network coding. It has since…

The Schwartz-Zippel Lemma is a fundamental tool, that provides a bound on the size of the zero set of multivariate polynomials.In this talk we present a classical proof of the Schwartz-Zippel Lemma…

Vladuts characterized in 1999 the set of finite fields k such that all elliptic curves defined over k have a cyclic group of rational points. Under the conjecture of infinitely many Mersenne primes,…

Minimal codewords of a linear code reveal its important structural properties and are required, for instance, in secret-sharing schemes and certain decoding algorithms. A nonzero codeword is said to…

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…