Related papers: LinCode -- computer classification of linear codes
In this paper, we introduce an efficient iterative solver for the joint linear-programming (LP) decoding of low-density parity-check (LDPC) codes and finite-state channels (FSCs). In particular, we extend the approach of iterative…
In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtained from…
In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes. As…
We survey recent generalizations and improvements of the linear programming method that involve semidefinite programming. A general framework using group representations and tools from graph theory is provided.
We develop an algorithm for computing the weight distribution of a linear $[n,k]$ code over a finite field $\mathbb{F}_q$. We represent the codes by their characteristic vector with respect to a given generator matrix and a special type of…
The goal of our Macro Lambda Calculus project (MLC) is to encode lambda terms into interaction nets. Its software implementation will accept input in the notation similar to lambda calculus allowing macro definitions. Output is similar to…
We introduce a novel approach to the automated termination analysis of computer programs: we use neural networks to represent ranking functions. Ranking functions map program states to values that are bounded from below and decrease as a…
A visibility algorithm maps time series into complex networks following a simple criterion. The resulting visibility graph has recently proven to be a powerful tool for time series analysis. However its straightforward computation is…
Linear layered probabilistic shaping (LLPS) is proposed, an architecture for linear codes to efficiently encode to shaped code words. In the previously proposed probabilistic amplitude shaping (PAS) architecture, a distribution matcher (DM)…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
We apply the semidefinite programming method to derive bounds for projective codes over a finite field.
We study a new class of codes over Z_2 x Z_2 which we call L-codes. They arise as a natural fifth step in a series of analogies between Kleinian codes, binary codes, lattices and vertex operator algebras. This analogy will be explained in…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
We propose an improved algorithm for finding roots of polynomials over finite fields. This makes possible significant speedup of the decoding process of Bose-Chaudhuri-Hocquenghem, Reed-Solomon, and some other error-correcting codes.
Large Language Models (LLMs) have demonstrated impressive capabilities in understanding and generating codes. Due to these capabilities, many recent methods are proposed to automatically refine the codes with LLMs. However, we should…
We present LTLS, a technique for multiclass and multilabel prediction that can perform training and inference in logarithmic time and space. LTLS embeds large classification problems into simple structured prediction problems and relies on…
As of today the programming language of the vast majority of the published source code is manually specified or programmatically assigned based on the sole file extension. In this paper we show that the source code programming language…
We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm which we used to obtain first examples of so-called non-easy linear categories of…