Modul:   MAT076  Neuchatel - St.Gallen - Zurich Seminar in Coding Theory and Cryptography

Analysis and Decoding of Linear Lee-Metric Codes with Application to Code-Based Cryptography

Vortrag von Jessica Bariffi

Datum: 24.04.24  Zeit: 15.15 - 16.15  Raum: Y27H25

In the last few decades, Lee-metric codes gained a lot of attention especially with their promising application to code-based cryptography as well as their connection to lattices. Even though, begin a rather old metric considered in coding theory, there are still many open questions regarding Lee metric codes regarding both the algebraic structure of codes in the Lee metric as well as efficient decoding algorithms. In this talk we present some selected topics on Lee-metric codes. We start by introducing generalized Lee distances in order to derive improved upper bounds on the minimum Lee distance. We discuss the derivation of the bound as well as the density of codes achieving it. In a next step we turn the attention to channel coding where we introduce two channel models in the Lee metric. At this point we specifically focus on a static channel model, introducing an error of fixed weight. We derive its marginal distribution using typical sequences. Additionally, this channel can be viewed as a design parameter to code-based cryptography and hence, the knowledge of the marginal distribution shows some implication in the field of cryptography too. Lastly, we introduce classical random low-density parity-check (LDPC) codes over a finite integer residue ring endowed with the Lee metric, and we present their expected weight enumerator.