## 1 Introduction
In [PERSON] _et al._ (2016); [PERSON] _et al._ (2016), the recursive code construction for binary covers was improved, and it was shown that the construction can achieve the rate-distortion bound. To improve RDH schemes based on the distortion matrices, a system estimating the optimal transition probability matrix for a general distortion matrix was proposed in [PERSON] _et al._ (2016). In the RDH system with histogram shift, the histogram was first produced by the error value between original pixels and estimated pixels. According to embedded data and the error value, the error histogram was shifted for saving space for data embedding by shifting the bins of the histogram. In [PERSON] _et al._ (2016), the RDH based on the histogram of the prediction vector quantization-compressed image was proposed where the index of the image was used for embedding. Similarly, [PERSON] (2015) proposed RDH systems for encrypted images by reserving room, where the original image was divided into two partitions and the LSBs of one partition were embedded into the other partition by a traditional RDH algorithm [PERSON] _et al._ (2016). In [PERSON] _et al._ (2016), generating RDH codes according to the theoretical expressions [PERSON] _et al._ (2016) of RDH were determined by the differences between the original pixel-values and the corresponding values estimated from the neighbors. An efficient RDH method was proposed by estimating pairwise prediction errors and modifying the 2D histogram of the prediction-errors in [PERSON] _et al._ (2016). Recently, [PERSON] _et al._ (2016) proposed a combination method with a histogram modification and lossless data compression by using an entropy coder. Recently, modified RDH systems were proposed to have better performance. Data hiding by using zero coefficient quantization table was proposed in JPEG images [PERSON] _et al._ (2016). [PERSON] et al. [PERSON] _et al._ (2016) introduced a hybrid data hiding method combining the right-most digit replacement (RMDR) with an adaptive least significant bit (ALSB) for digital images. [PERSON] et al. [PERSON] _et al._ (2016) proposed RDH based on prediction error and expansion based on adjacent pixels. [PERSON] et al. [PERSON] _et al._ (2016) proposed a new data-hiding technique for absolute moment block truncation coding (AMBTC) of a compressed image based on quantization level modification. Improved embedding pattern and a new measurement function were proposed in encrypted images with a high payload to enhance transmission performance [PERSON] _et al._ (2016). One vacating room before encryption was proposed in encrypted image, where the content owner creates room for embedding data in the cover image before encryption [PERSON] _et al._ (2016). [PERSON] et al. [PERSON] _et al._ (2016) proposed a novel scheme of RDH in encrypted images using distributed source coding to protect the secrecy of the system. [PERSON] et al. [PERSON] _et al._ (2016) proposed a separable RDH technique in encrypted images based on the pixel value ordering where homomorphism encryption is used for image encryption. The Reed-Solomon (RS) codes are named for their inventors who published the codes in 1960. RS codes have good error-correction capability for bursty errors since they are non-binary cyclic maximum distance separable codes. Therefore, they have been widely used in consumer electronics, data transmission technologies, broadcast systems, optical communications and image processing systems. During the past decades, research about RS codes has been updated quickly. The Berlekamp-Massey (BM) algorithm [PERSON] (1960) is an efficient hard decoding algorithm of RS codes that uses a linear feedback shift register (LFSR) to determine error location polynomials with the smallest degree and error locations by solving the roots of the polynomials. A new run-length-limited decoding algorithm to increase the performance of RS codes in a visible light communication system has been proposed [PERSON] and [PERSON] (1960).