Related papers: On Codes and Learning With Errors over Function Fi…
Linear codes over finite fields parameterized by functions have proven to be a powerful tool in coding theory, yielding optimal and few-weight codes with significant applications in secret sharing, authentication codes, and association…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
Low decoding latency and complexity are two important requirements of channel codes used in many applications, like machine-to-machine communications. In this paper, we show how these requirements can be fulfilled by using some special…
Reinforcement learning (RL) offers a capable and intuitive structure for the fundamental sequential decision-making problem. Despite impressive breakthroughs, it can still be difficult to employ RL in practice in many simple applications.…
Low Rank Parity Check (LRPC) codes form a class of rank-metric error-correcting codes that was purposely introduced to design public-key encryption schemes. An LRPC code is defined from a parity check matrix whose entries belong to a…
A system is offered for imitation resistant transmitting of encrypted information in wireless communication networks on the basis of redundant residue polynomial codes. The particular feature of this solution is complexing of methods for…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
This paper presents CodeRefine, a novel framework for automatically transforming research paper methodologies into functional code using Large Language Models (LLMs). Our multi-step approach first extracts and summarizes key text chunks…
We propose a framework for constructing efficient code-based encryption schemes from codes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based…
Let $X_1, ..., X_m$ be a set of $m$ statistically dependent sources over the common alphabet $\mathbb{F}_q$, that are linearly independent when considered as functions over the sample space. We consider a distributed function computation…
A new approach for decoding binary linear codes by solving a linear program (LP) over a relaxed codeword polytope was recently proposed by Feldman et al. In this paper we investigate the structure of the polytope used in the LP relaxation…
In rank-metric cryptography, a vector from a finite dimensional linear space over a finite field is viewed as the linear space spanned by its entries. The rank decoding problem which is the analogue of the problem of decoding a random…
The advent of quantum computing necessitates the transition of worldwide cryptosystems to post-quantum cryptography (PQC), which is founded upon the problem of finding short vectors in high-dimensional structured lattices. It is assumed…
The learning parity with noise (LPN) problem is a well-established computational challenge whose difficulty is critical to the security of several post-quantum cryptographic primitives such as HQC and Classic McEliece. Classically, the…
A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…
We analyse the number of occurrences of a fixed non-zero digit in the width-w non-adjacent forms of all elements of a lattice in some region (e.g. a ball). Our result is an asymptotic formula, where its main term coincides with the full…
We introduce a framework generalizing lattice reduction algorithms to module lattices in order to practically and efficiently solve the $\gamma$-Hermite Module-SVP problem over arbitrary cyclotomic fields. The core idea is to exploit the…
We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…
The rank decoding problem has been the subject of much attention in this last decade. This problem, which is at the base of the security of public-key cryptosystems based on rank metric codes, is traditionally studied over finite fields.…
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and…