Reed-Solomon codes are examples of error correcting codes, in which redundant information is added to data so that it can be recovered reliably despite errors in transmission or storage and retrieval. The error correction system used on CD’s and DVD’s is based on a Reed-Solomon code. These codes are also used on satellite links and other communications systems. We will first discuss the general...

The purpose of this paper is to study and analyze the performance and efficiency of Reed Solomon (RS) coding. In coding theory, Reed Solomon codes are the subset of BCH codes that are one of the most powerful known classes of linear cyclic block codes. Reed Solomon (RS) codes are very efficient and best for correction of burst errors and have a wide range of applications in digital communicatio...

Because of their importance in applications and their quite simple definition, Reed–Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed– Solomon codes are far from being simple and it is difficult to fit them in introductory courses for undergraduates. We introduce a new decoding approach, in a self-contained presentation, which we t...

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...

The Schmidt–Sidorenko–Bossert scheme extends a low-rate Reed–Solomon code to an Interleaved Reed–Solomon code and achieves the decoding radius of Sudan’s original list decoding algorithm while the decoding result remains unambiguous. We adapt this result to the case of Generalized Reed– Solomon codes and calculate the parameters of the corresponding Interleaved Generalized Reed–Solomon code. Fu...

In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.

MDS (e.g. Reed-Solomon) codes have many desirable properties which make them the code of choice in network scenarios and distributed coding schemes. An average binary weight enumerator of Reed-Solomon (RS) codes is derived assuming a binomial distribution of the bits in a non-zero symbol. Lower bounds on the average binary minimum distance of the ensemble of binary images of a Reed-Solomon code...

Reed-Solomon and BCH codes were considered as kernels of polar codes by Mori and Tanaka in [6] and Korada, Şaşoğlu, and Urbanke in [4] to create polar codes with large exponents. For codes of length l ≤ q, Mori and Tanaka showed Reed-Solomon codes give the best possible exponent, where q is the size of the input alphabet. However, considering larger matrices over Fq yields better exponents for ...

Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study upper bounds for separating codes. First, some new upper bound for restricted separating codes is proposed. Then we illustrate that the Upper Bound Conjecture f...

During the last years it has been shown that computers taking advantage of quantum mechanical phenomena outperform currently used computers. The striking examples are integer factoring in polynomial time (see [8]) and finding pre– images of an n–ary Boolean function (“searching”) in time O( √ 2n) (see [5]). Quantum computers are not only of theoretical nature—there are several suggestions how t...