Polynomial remainder codes are a large class of codes derived from the Chinese remainder theorem that includes Reed-Solomon codes as a special case. In this paper, we revisit these codes and study them more carefully than in previous work. We explicitly allow the code symbols to be polynomials of different degrees, which leads to two different notions of weight and distance. Algebraic decoding ...

In this paper a characterization of the general relation between linear multisecret-sharing schemes and error-correcting codes is presented. A bridge between linear multisecret-sharing threshold schemes and maximum distance separable codes is set up. The information hierarchy of linear multisecret-sharing schemes is also established. By making use of the bridge several linear multisecret-sharin...

Two architecturesfor universal Reed-Solomon decoders are given. These decoders, called time-domain decoders, work directly on the raw data word as received without the usual syndrome calculation or power-sum-symmetric functions Up to the limitations of the working registers, the decoders can decode any Reed-Solomon codeword or BCH codeword in the presence of both errors and erasures. Provision ...

The interpolation step of Sudan’s list decoding of Reed-Solomon codes sets forth the problem of finding the minimal polynomial of an ideal with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Gröbner bases of modules. In a special case, this algorithm is shown to be equivalent with the Berlekamp-Massey algorithm for decodin...

In this paper, deep holes of Reed-Solomon (RS) codes are studied. A new class of deep holes for generalized affine RS codes is given if the evaluation set satisfies certain combinatorial structure. Three classes of deep holes for projective Reed-Solomon (PRS) codes are constructed explicitly. In particular, deep holes of PRS codes with redundancy three are completely obtained when the character...

Abstract. The subset sum problem over finite fields is a well-known NPcomplete problem. It arises naturally from decoding generalized Reed-Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a mathematical point of view. In several interesting cases, we obtain explicit or asymptotic formulas for the solution number. As a consequence, we obtain some resu...

The interpolation step of Sudan’s list decoding of Reed-Solomon codes sets forth the problem of finding the minimal polynomial of the ideal of interpolating polynomials with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Gröbner bases of modules. In a special case, this algorithm is shown to be equivalent with the Berlekam...

From: TM Synchronization and Channel Coding is used to protect the transfer frames against telemetry channel noise‐induced errors. Reference [3] describes the CCSDS Recommended Standard for TM Synchronization and Channel Coding, including specification of a convolutional code, a Reed‐ Solomon block‐oriented code, a concatenated coding system consisting of a convolutional inner code and a Reed‐S...

Title of dissertation: PERFORMANCE ANALYSIS OF ALGEBRAIC SOFT-DECISION DECODING OF REED-SOLOMON CODES Andrew Duggan, Masters of Science, 2006 Thesis directed by: Professor Alexander Barg Department of Electrical and Computer Engineering We investigate the decoding region for Algebraic Soft-Decision Decoding (ASD) of Reed-Solomon codes in a discrete, memoryless, additive-noise channel. An expres...

In this paper, construction of partitioned Reed Solomon coded modulation (RSCM), which is robust for the additive white Gaussian noise channel and a Rayleigh fading channel, is investigated. By matching configuration of component codes with the channel characteristics, it is shown that this system is robust for the Gaussian and a Rayleigh fading channel. This approach is compared with non-parti...