Related papers: Inference of unknown syndrome values in the implem…
This paper proposes a novel algorithm for finding error-locators of algebraic-geometric codes that can eliminate the division-calculations of finite fields from the Berlekamp-Massey-Sakata algorithm. This inverse-free algorithm provides…
For Reed-Solomon codes, the key equation relates the syndrome polynomial---computed from the parity check matrix and the received vector---to two unknown polynomials, the locator and the evaluator. The roots of the locator polynomial…
We study the computation of error values in the decoding of codes constructed from order domains. Our approach is based on a sort of analog of the key equation for decoding Reed-Solomon and BCH codes. We identify a key equation for all…
An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine variety codes is proposed. Our procedure is achieved by…
We propose a new algorithm for decoding Reed-Solomon codes (up to half the minimum distance) and for computing inverses in $F[x]/m(x)$. The proposed algorithm is similar in spirit and structure to the Berlekamp-Massey algorithm, but it…
This article is focused on some variations of Reed-Muller codes that yield improvements to the rate for a prescribed decoding performance under the Berlekamp-Massey-Sakata algorithm with majority voting. Explicit formulas for the…
The two primary decoding algorithms for Reed-Solomon codes are the Berlekamp-Massey algorithm and the Sugiyama et al. adaptation of the Euclidean algorithm, both designed to solve a key equation. In this article an alternative version of…
We deal with two problems related with the use of the Sakata's algorithm in a specific class of bivariate codes. The first one is to improve the general framework of locator decoding in order to apply it on such abelian codes. The second…
Analysis of the Berlekamp-Massey-Sakata algorithm for decoding one-point codes leads to two methods for improving code rate. One method, due to Feng and Rao, removes parity checks that may be recovered by their majority voting algorithm.…
We study the problem of the computation of Groebner basis for the ideal of linear recurring relations of a doubly periodic array. We find a set of indexes such that, along with some conditions, guarantees that the set of polynomials…
We compare thoroughly the Berlekamp -- Massey -- Sakata algorithm and the Scalar-FGLM algorithm, which compute both the ideal of relations of a multi-dimensional linear recurrent sequence. Suprisingly, their behaviors differ. We detail in…
The Welch--Berlekamp approach for Reed--Solomon (RS) codes forms a bridge between classical syndrome--based decoding algorithms and interpolation--based list--decoding procedures for list size l=1. It returns the univariate error--locator…
In this paper, a new algebraic soft-decision decoding algorithm for Reed-Solomon code is presented. It is based on rational interpolation and the interpolation points are constructed by Berlekamp-Messay algorithm. Unlike the traditional…
Codes in the sum-rank metric have various applications in error control for multishot network coding, distributed storage and code-based cryptography. Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as…
Missing values are a fundamental problem in data science. Many datasets have missing values that must be properly handled because the way missing values are treated can have large impact on the resulting machine learning model. In medical…
Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and…
In this paper, a new approach for decoding low-rate Reed-Solomon codes beyond half the minimum distance is considered and analyzed. Unlike the Sudan algorithm published in 1997, this new approach is based on multi-sequence shift-register…
Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of…
Garcia-Donato et al. (2025) present a methodology for handling missing data in a model selection problem using an objective Bayesian approach. The current comment discusses an alternative, existing objective Bayesian method for this…
Nonignorable missing outcomes are common in real world datasets and often require strong parametric assumptions to achieve identification. These assumptions can be implausible or untestable, and so we may forgo them in favour of partially…