Coding Theory and Cryptography Seminars
Coding Theory and Cryptography Seminars
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We propose the new rank-metric code-based cryptosystem LIGA which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes. LIGA is an…
Antonia Wachter-Zeh: LIGA - A Cryptosystem Based…
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Questions on solutions of polynomial equations over finite fields have a long history and occupy an important place in number theory. In this talk we will be interested…
Recursive Towers over Finite Fields
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Quasi-cyclic (QC) linear codes over finite fields constitute an important class of linear block codes. They are a remarkable generalization of cyclic codes and, in…
Quasi-cyclic Codes: An overview
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Among the most studied invariants for linear block codes, there are the generalized weights. The interest in these invariants stems from the fact that they measure…
Generalized weights of convolutional codes
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Reed-Solomon codes are a well-known technique to represent data in the form of vectors, such that the data can be recovered even if some vector coordinates are…
Computing Riemann-Roch spaces for algebraic…
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We present a novel approach to non-adaptive group testing by modelling it in terms of residuated pairs on partially ordered sets. The resulting efficient decision scheme…
Error-Correcting Group Testing and Residuation…
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Physical channels like the internet are highly used in the modern world. The impact of the corona pandemic and the current age of digitisation even increased this usage…
Constructions of Rank Metric Convolutional Codes…
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This talk presents an information-theoretic study of the rate-performance tradeoffs in distributed hypothesis testing, with a particular focus on systems with average…
Information-Theoretic Tradeoffs in Distributed…
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In this talk, we present a unifying framework to construct low-density parity-check (LDPC) codes with associated Tanner graphs of desired girth. Towards this goal, we…
A Unifying Framework to Construct QC-LDPC Tanner…
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Packet channels are subject to packet losses and these can be modeled as packet erasures where we know the lost packet's location but not its content. Channel…
Coding for packet erasure channels
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Linear sets are a natural generalization of projective subspaces and of subgeometries in a projective space over a finite field. They were introduced by Lunardon in 1999…
Linear sets in coding theory
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In this talk we study the dual and the algebraic dual of an evaluation code using standard monomials and indicator functions. We show that the dual of an evaluation code…
eSeminar: The dual of an evaluation code
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eSeminar: Parameters of Codes for the Binary… 13 of 36
eSeminar: Parameters of Codes for the Binary…
Binary asymmetric channels are channels over the binary alphabet {0,1}, in which the probability that a 0 becomes a 1 and the probability that a 1 becomes a 0 are…eSeminar: Parameters of Codes for the Binary…
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Linearized Reed-Solomon (LRS) codes are sum-rank-metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they…
eSeminar: Bounds on List Decoding of Linearized…
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This talk is about algorithms for modular composition of univariate polynomials, and for computing minimal polynomials. For two univariate polynomials a and g over a…
eSeminar: Faster modular composition of…
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There are several convenient ways to construct quantum codes from classical codes, the CSS and Hermitian construction are two popular among them. Here, we describe how…
eSeminar: Construction of Quantum Codes using…
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eSeminar: EHT public-key crypto-system and…
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With advancements in quantum computing, the search for efficient algorithms for synthesising gates (the building blocks of quantum algorithms) using cost-effective gate…
eSeminar: Connections between cryptography and…
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eSeminar: Automorphisms of Cyclic Orbit Codes 19 of 36
eSeminar: Automorphisms of Cyclic Orbit Codes
Cyclic orbit codes are a prominent class of subspace codes, generated by taking the orbit of a single subspace of the finite field $F_{q^n}$ under an action of a Singer…eSeminar: Automorphisms of Cyclic Orbit Codes
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Consider $C$, an $[n,k,d]$-linear code. Every projective codeword of minimum weight $d$ corresponds to a point in $\mathbb P^{k-1}$, and there are b connections between…
Linear codes with prescribed projective codewords…
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An open question in coding theory asks whether or not MRD codes with the rank metric are dense as the field size tends to infinity. In this talk, I will briefly survey…
The Sparseness of MRD Codes
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Constructions of Codes in the Sum-Rank Metric 22 of 36
Constructions of Codes in the Sum-Rank Metric
The sum-rank metric simultaneously extends the Hamming metric and the rank metric. Thus it provides a general theory that includes both classical and rank-metric codes.…Constructions of Codes in the Sum-Rank Metric
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In this talk, I will present the recent improvements inalgebraic techniques for solving the MinRank problem, which isubiquitous in multivariate and rank metric code…
Algebraic Attacks for solving the Rank Decoding…
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Classification and Construction of Self-Dual… 24 of 36
Classification and Construction of Self-Dual…
Self-dual convolutional codes are codes, for which the set of vectors that are orthogonal to every codeword is exactly the code itself. Our main goal will be to…Classification and Construction of Self-Dual…
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In this talk, we discuss the problem of outsourcing computations to untrusted servers in multiple settings (i.e., multiple clients, multiple servers). More precisely, we…
Katerina Mitrokotsa: Outsourcing computations to…
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The uncertainty principle is a very famous inequality in Physics, Signal Processing, and Harmonic Analysis. It compares the supports of functions and of their…
Martino Borello: Asymptotic performance of…
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In this talk, beginning with the original construction of polar codes, we explore the monomial decreasing codes as a generalization of those in channels with b symmetry.…
Eduardo Camps: Monomial Decreasing Codes
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Let PG(r, q) be the r-dimensional projective space over the finite field GF(q). A set Χ of points of PG(r, q) is a cutting blocking set if for each hyperplane Π…
Francesco Pavese: On cutting blocking sets and…
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In this talk, I will introduce a new variant, MP-LWE, of the Learning With Errors problem (LWE) making use of the Middle Product between polynomials modulo an integer q.…
Amin Sakzad: Middle-product learning with errors…
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The concept of tensor products is ubiquitous in the scientific literature. In this talk, we restrict our attention to the tensor product of a finite number of…
Michel Lavrauw: Tensors in Finite Geometry
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Communication of data on electrical wires between chips is fast gaining prominence in the electronics industry. Because most of the components of the transmitter and the…
Amin Shokrollahi: Chord Signaling
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The central objects of this talk are univariate polynomials over finite fields. We survey methods and results to count polynomials satisfying certain properties, and to…
Daniel Panario: Analytic and Probabilistic…
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In this talk, we give an overview of combinatorial designs, their q-analogues and related structures. Design theory has a venerable history starting in the 1830s. The…
Alfred Wassermann: Designs, subspace designs and…
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We propose the new rank-metric code-based cryptosystem LIGA which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes. LIGA is an…
Antonia Wachter-Zeh: LIGA - A Cryptosystem Based…
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AbstractA quantum error-correcting code (QECC), denoted by ((n,K,d))_q, is a K-dimensional subspace of the complex vector space C^(q^⊗n) that is able to correct…
Markus Grassl - On Quantum MDS Codes
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The Minrank (MR) problem is a computational problem closely related to attacks on code- and multivariate-based schemes. MR can be reduced to a bilinear system of…
Daniel Cabarcas: From Minrank Attack to generic…
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