Search

A linear complementary dual (LCD) code is a linear code with complimentary dual. LCD codes have been extensively studied in literature. On the other hand, maximum distance separable (MDS) codes are an important class of linear codes that have found wide applications in both theory and practice. However, little is known about MDS codes with complimentary duals. The main purpose of this paper is to construct several classes of MDS codes with complimentary duals, i.e., LCD MDS codes, through generalized Reed-Solomon codes. [ABSTRACT FROM PUBLISHER]

In distributed storage, erasure codes (like Reed–Solomon Codes) are often employed to provide reliability. In this setting, it is desirable to be able to repair one or more failed nodes while minimizing the repair bandwidth. In this paper, motivated by Reed-Solomon codes, we study the problem of repairing multiple failed nodes in a scalar MDS code. We extend the framework of (Guruswami and Wootters, 2017) to give a framework for constructing repair schemes for multiple failures in general scalar MDS codes in the centralized repair model. We then specialize our framework to Reed–Solomon codes, and also extend and improve upon recent results of (Dau et al., 2017). [ABSTRACT FROM AUTHOR]

Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This application of LCD codes renewed the interest in the construction of LCD codes having a large minimum distance. Maximum distance separable (MDS) codes are optimal in the sense that the minimum distance cannot be improved for given length and code size. Constructing LCD MDS codes is thus of significance in theory and practice. Recently, Jin constructed several classes of LCD MDS codes through generalized Reed-Solomon codes. In this paper, a different approach is proposed to obtain new LCD MDS codes from generalized Reed-Solomon codes. Consequently, new code constructions are provided and certain previously known results by Jin are extended. [ABSTRACT FROM AUTHOR]

A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the encoding is a function of a small number (at most \(r\) ) other symbols. We present a family of LRC codes that attain the maximum possible value of the distance for a given locality parameter and code cardinality. The codewords are obtained as evaluations of specially constructed polynomials over a finite field, and reduce to a Reed-Solomon code if the locality parameter \(r\) is set to be equal to the code dimension. The size of the code alphabet for most parameters is only slightly greater than the code length. The recovery procedure is performed by polynomial interpolation over \(r\) points. We also construct codes with several disjoint recovering sets for every symbol. This construction enables the system to conduct several independent and simultaneous recovery processes of a specific symbol by accessing different parts of the codeword. This property enables high availability of frequently accessed data (“hot data”). [ABSTRACT FROM PUBLISHER]