Journal of the Society for Industrial and Applied Mathematics. In June of 1960 the paper was published: five pages under the rather unpretentious title "Polynomial Codes over Certain Finite Fields" [17]. This paper described a new class of error-correcting codes that are now called Reed-Solomon codes. In the decades since their discovery, Reed-Solomon codes have enjoyed countless applications, ...

In Reed-Solomon codes and all other maximum distance separable codes, there is an intrinsic relationship between the size of the symbols in a codeword and the length of the codeword. Increasing the number of symbols in a codeword to improve the efficiency of the coding system thus requires using a larger set of symbols. However, long Reed-Solomon codes are difficult to implement and many commun...

In this paper we present a modification of Reed-Solomon codes that beats the GuruwamiSudan 1− √ R decoding radius of Reed-Solomon codes at low rates R. The idea is to choose Reed-Solomon codes U and V with appropriate rates in a (U | U + V ) construction and to decode them with the Koetter-Vardy soft information decoder. We suggest to use a slightly more general version of these codes (but whic...

in-service education programs have provided the professional development level of companies' employers, in the high quality form. the applying of in-service education programs has been a key component of professional development process for staff agro-industry company. the study is utilized experimental solomon four group designs to determine the impact of in-service education programs on agro-...

Interleaved Reed–Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed–Solomon codes. Usually, these codewords are decoded independently by classical algebraic decoding methods. However, by collaborative algebraic decoding approaches, such interleaved schemes allow the correction ...

he main aim of this paper is to give some essential background to the theory of Reed Solomon codes and the previous survey literature of the Reed Solomon error correction method using various algorithm.Reed Solomon codes have shown to be the best compromise between efficiency and complexity. These are cyclic codes and are used for the detection and correction of burst errors. Galois field is us...

Author Contributions:Dr Loprinzi had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Study concept and design: Loprinzi, Brodowicz. Acquisition, analysis, or interpretation of data: Loprinzi, Sengupta, Solomon, Ramulu. Drafting of the manuscript: Loprinzi, Brodowicz. Critical revision of the manuscript for...

Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word u is a deep hole of the standard Reed-Solomon codes [q− 1, k]q if its Lagrange interpolation polynomial is the sum of monomial of degree q− 2 and a polynomial of degree at most k− 1. In this paper, we extend this result by giving a new class of deep holes of the...

We propose to reduce the decoding complexity of polar codes with non-Arikan kernels by employing a (near) ML decoding algorithm for the codes generated by kernel rows. A generalization of the order statistics algorithm is presented for soft decoding of Reed-Solomon codes. Algebraic properties of the Reed-Solomon code are exploited to increase the reprocessing order. The obtained algorithm is us...

395 Abstract—Reed-Solomon Codes are popularly used for error correction in many applications like storage devices (CD, DVD), wireless communications, high speed modems and satellite communications. In this paper, a modified scheme for programmable generator polynomial based Reed-Solomon encoder and decoder has been proposed. The works reported in this paper corrects errors in derived equations ...