Under polynomial time reduction, the maximun likelihood decoding of a linear code is equivalent to computing the error distance of a received word. It is known that the decoding complexity of standard Reed-Solomon codes at certain radius is at least as hard as the discrete logarithm problem over certain large finite fields. This implies that computing the error distance is hard for standard Ree...

Codes with traceability properties are used in schemes where the identification of users that illegally redistribute content is required. For any code with traceability properties, the Identifiable Parent Property (c-IPP) seems to be less restrictive than the Traceability (c-TA) property. In this paper, we show that for Reed-Solomon codes both properties are in many cases equivalent. More preci...

Both linear complementary dual (LCD) codes and maximum distance separable (MDS) have good algebraic structures, they interesting practical applications such as communication systems, data storage, quantum codes, so on. So far, most of LCD MDS been constructed by employing generalized Reed-Solomon codes. In this paper we construct some classes new Euclidean Hermitian which are not monomially equ...

Reed-Solomon codes were formally introduced to the world in 1960, and have been both practically and theoretically interesting since their introducion. Used in CD players, long-distance space communication, and computer networks, these simple codes have fascinated coding theorists and theoretical computer scientists for nearly five decades. In addition to being one of the Maximum Distance Seper...

We consider the repair problem for Reed–Solomon (RS) codes, evaluated on an $\mathbb {F}_{q}$ -linear subspace notation="LaTeX">$U\subseteq \mathbb {F}_{q^{m}} $ of dimension notation="LaTeX">$d$ , where notation="LaTeX">$q$ is a prim...

A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches are proposed. In particular, both the decoding approaches by means of a fixed transform are treated in a way compatible with the error-only decoding. In the...

Errors occur after the transmission, because of noise and intervention in communication channels. Protecting digital information is very important with a suitable error-control code that enables the efficient detection and correction of any errors that may have occurred. Error-control codes are now used in the entire range of communication. New types of codes, called Reed –Solomon have been dev...

Network transfer and disk read are the most time consuming operations in the repair process for node failures in erasure-code-based distributed storage systems. Recent developments on Reed-Solomon codes, the most widely used erasure codes in practical storage systems, have shown that efficient repair schemes specifically tailored to these codes can significantly reduce the network bandwidth spe...

We propose an alternative method for collaborative decoding of interleaved Reed-Solomon codes. Simulation results for a concatenated coding scheme using polar codes as inner codes are included.