Related papers: List-decoding of AG codes without genus penalty
The Grassmannian is an important object in Algebraic Geometry. One of the many techniques used to study the Grassmannian is to build a vector space from its points in the projective embedding and study the properties of the resulting linear…
Consider an ensemble of regular generalized LDPC (GLDPC) codes and assume that the same component code is associated with each parity check node. To decode a GLDPC code from the ensemble, we use the bit flipping bounded distance decoding…
Scene Graph Generation (SGG) aims to generate a comprehensive graphical representation that accurately captures the semantic information of a given scenario. However, the SGG model's performance in predicting more fine-grained predicates is…
We develop a framework for solving polynomial equations with size constraints on solutions. We obtain our results by showing how to apply a technique of Coppersmith for finding small solutions of polynomial equations modulo integers to…
We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer…
Cell formation is a critical step in the design of cellular manufacturing systems. Recently, it was tackled using a cut-based-graph-partitioning model. This model meets real-life production systems requirements as it uses the actual amount…
We analyze the Guruswami--Sudan list decoding algorithm for Reed--Solomon codes over the complex field for sparse recovery in Compressed Sensing. We propose methods of stabilizing both the interpolation and the root-finding steps against…
We propose a method for generating explainable rule sets from tree-ensemble learners using Answer Set Programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in…
We give a complete answer to the following basic question: "What is the maximal fraction of deletions or insertions tolerable by $q$-ary list-decodable codes with non-vanishing information rate?" This question has been open even for binary…
An identifying open code of a graph $G$ is a set $S$ of vertices that is both a separating open code (that is, $N_G(u) \cap S \ne N_G(v) \cap S$ for all distinct vertices $u$ and $v$ in $G$) and a total dominating set (that is, $N(v) \cap S…
In this work we consider the list-decodability and list-recoverability of arbitrary $q$-ary codes, for all integer values of $q\geq 2$. A code is called $(p,L)_q$-list-decodable if every radius $pn$ Hamming ball contains less than $L$…
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…
For the category of group codes, that generalizes the category of linear codes over a finite field, and with the generalized notions of direct sums and ndecomposable group codes, we prove that every MDS non trivial code, every perfect non…
The parameters of the AG codes on general linear groups are found. The hyperplane sections having the minimum (or maximum) number of rational points are determined.
We study certain combinatorial aspects of list-decoding, motivated by the exponential gap between the known upper bound (of $O(1/\gamma)$) and lower bound (of $\Omega_p(\log (1/\gamma))$) for the list-size needed to decode up to radius $p$…
We study uniquely decodable codes and list decodable codes in the high-noise regime, specifically codes that are uniquely decodable from $\frac{1-\varepsilon}{2}$ fraction of errors and list decodable from $1-\varepsilon$ fraction of…
In a recent paper [1] an improved analysis concerning the analysis of List Decoding was presented. The event that the correct codeword is excluded from the list is central. For the additive white Gaussian noise (AWGN) channel an important…
We develop a package using the computer algebra system GAP for computing the decomposition of a representation $\rho$ of a finite group $G$ over $\mathbb{C}$ into irreducibles, as well as the corresponding decomposition of the centraliser…
We give a new framework based on graph regularity lemmas, for list decoding and list recovery of codes based on spectral expanders. Using existing algorithms for computing regularity decompositions of sparse graphs in (randomized)…
The paper concerns a certain subcategory of the category of representations for a semisimple algebraic group $G$ in characteristic $p$, which arise from the semisimple modules for the corresponding quantum group at a $p$-th root of unity.…