Related papers: On a linear code from a configuration of affine li…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
The problem of finding good linear codes for joint source-channel coding (JSCC) is investigated in this paper. By the code-spectrum approach, it has been proved in the authors' previous paper that a good linear code for the authors' JSCC…
We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. We determine the length, dimension, and the minimum…
Lifted Reed-Solomon codes are a natural affine-invariant family of error-correcting codes which generalize Reed-Muller codes. They were known to have efficient local-testing and local-decoding algorithms (comparable to the known algorithms…
A general lossless joint source-channel coding scheme based on linear codes is proposed and then analyzed in this paper. It is shown that a linear code with good joint spectrum can be used to establish limit-approaching joint source-channel…
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.
The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
I present the Automated Line Fitting Algorithm, ALFA, a new code which can fit emission line spectra of arbitrary wavelength coverage and resolution, fully automatically. In contrast to traditional emission line fitting methods which…
We show that, for every linear ordering of $[2]^n$, there is a large subcube on which the ordering is lexicographic. We use this to deduce that every long sequence contains a long monotone subsequence supported on an affine cube. More…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
In this paper, we present a construction of linear codes over $\f_{2^t}$ from Boolean functions, which is a generalization of Ding's method \cite[Theorem 9]{Ding15}. Based on this construction, we give two classes of linear codes…
Some linear codes associated to maximal algebraic curves via Feng-Rao construction are investigated. In several case, these codes have better minimum distance with respect to the previously known linear codes with same length and dimension.
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
We give a method to construct Locally Recoverable Error-Correcting codes. This method is based on the use of rational maps between affine spaces. The recovery of erasures is carried out by Lagrangian interpolation in general and simply by…
In this paper, we study the tradeoffs between complexity and reliability for decoding large linear block codes. We show that using artificial neural networks to predict the required order of an ordered statistics based decoder helps in…
In this note we prove a decomposition related to the affine fundamental group and the projective fundamental group of a line arrangement and a reducible curve with a line component. We give some applications to this result.
Matrix code allows one to discover algorithms and to render them in code that is both compilable and is correct by construction. In this way the difficulty of verifying existing code is avoided. The method is especially important for…
In this manuscript, we introduce a new class of linear codes, called affine symplectic Grassmann codes, and determine their parameters, automorphism group, minimum distance codewords, dual code and other key features. These linear codes are…
J. Y. Hyun, et al. (Des. Codes Cryptogr., vol. 88, pp. 2475-2492, 2020) constructed some optimal and minimal binary linear codes generated by one or two order ideals in hierarchical posets of two levels. At the end of their paper, they left…