Related papers: Decoding of Differential AG Codes
We present the first known efficient decoding algorithm for correcting multiple insertion-deletion errors in Helberg codes and their non-binary generalizations, extending a known algorithm for correcting multiple deletion errors.
Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications.…
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
The recently-discovered polar codes are widely seen as a major breakthrough in coding theory. These codes achieve the capacity of many important channels under successive cancellation decoding. Motivated by the rapid progress in the theory…
Polar codes are a recently proposed family of provably capacity-achieving error-correction codes that received a lot of attention. While their theoretical properties render them interesting, their practicality compared to other types of…
In this work we investigate the problem of producing iso-dual algebraic geometry (AG) codes over a finite field $\mathbb{F}_q$ with $q$ elements. Given a finite separable extension $\mathcal{M}/\mathcal{F}$ of function fields and an…
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including…
Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…
We obtain a new coding and decoding method using the generalized Pell $(p,i)$ -numbers. The relations among the code matrix elements, error detection and correction have been established for this coding theory. We give two new blocking…
The Goppa Code Distinguishing (GD) problem asks to distinguish efficiently a generator matrix of a Goppa code from a randomly drawn one. We revisit a distinguisher for alternant and Goppa codes through a new approach, namely by studying the…
We define a new class of Convolutional Codes in terms of fibrations of algebraic varieties generalizaing our previous constructions of Convolutional Goppa Codes. Using this general construction we can give several examples of Maximum…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
Craig interpolation is used in program verification for automating key tasks such as the inference of loop invariants and the computation of program abstractions. This chapter covers some of the most important techniques that have been…
Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…
A class of linear codes that extends classic Goppa codes to a non-commutative context is defined. An efficient decoding algorithm, based on the solution of a non-commutative key equation, is designed. We show how the parameters of these…
In this paper, we propose an analysis of the automorphism group of polar codes, with the scope of designing codes tailored for automorphism ensemble (AE) decoding. We prove the equivalence between the notion of decreasing monomial codes and…
Deep learning methods have recently been used to construct non-linear codes for the additive white Gaussian noise (AWGN) channel with feedback. However, there is limited understanding of how these black-box-like codes with many learned…