Abstract—Novel encoding scheme for algebraic codes, such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed–Solomon codes, is proposed with numerical examples. We make use of the 2-dimensional inverse discrete Fourier transform, which generalizes the Mattson–Solomon polynomial for Reed–Solomon codes. We also generalize the workings of the generator polynom...

In this paper we investigate the structure of quasi-BCH codes. In the first part of this paper we show that quasi-BCH codes can be derived from Reed-Solomon codes over square matrices extending the known relation about classical BCH and Reed-Solomon codes. This allows us to adapt the Welch-Berlekamp algorithm to quasi-BCH codes. In the second part of this paper we show that quasi-BCH codes can ...

A new class of cyclic codes that is Reed-Solomon codes are discussed for IEEE 802.16 wireless networks. Reed-Solomon codes are used for the error detection and correction in communication systems. This is important in information theory and coding to correct burst errors. Here Reed-Solomon code for wireless network 802.16 is synthesized using VHDL on Xilinx and simulated on ISE simulator. The R...

Abstract This paper proposes a new class of multi-dimensional nonsystematic Reed-Solomon codes that are constructed based on the multi-dimensional Fourier transform over a finite field. The proposed codes are the extension of the nonsystematic Reed-Solomon codes to multi-dimension. This paper also discusses the performance of the multidimensional nonsystematic Reed-Solomon codes.

Deep holes play an important role in the decoding of generalized Reed-Solomon codes. Recently, Wu and Hong [11] found a new class of deep holes for standard Reed-Solomon codes. In the present paper, we give a concise method to obtain a new class of deep holes for generalized Reed-Solomon codes. In particular, for standard Reed-Solomon codes, we get the new class of deep holes given in [11]. Li ...

In this paper we present a modification of Reed-Solomon codes that beats the GuruwamiSudan 1− √ R decoding radius of Reed-Solomon codes at low rates R. The idea is to choose Reed-Solomon codes U and V with appropriate rates in a (U | U + V ) construction and to decode them with the Koetter-Vardy soft information decoder. We suggest to use a slightly more general version of these codes (but whic...

Journal of the Society for Industrial and Applied Mathematics. In June of 1960 the paper was published: five pages under the rather unpretentious title "Polynomial Codes over Certain Finite Fields" [17]. This paper described a new class of error-correcting codes that are now called Reed-Solomon codes. In the decades since their discovery, Reed-Solomon codes have enjoyed countless applications, ...

In this article, we present a new construction of evaluation codes in the Hamming metric, which call twisted Reed–Solomon codes. Whereas Reed–Solomon (RS) are MDS codes, need not be case for twisted RS Nonetheless, show that our yields several families Further, large subclass (MDS) generalized ...

In Reed-Solomon codes and all other maximum distance separable codes, there is an intrinsic relationship between the size of the symbols in a codeword and the length of the codeword. Increasing the number of symbols in a codeword to improve the efficiency of the coding system thus requires using a larger set of symbols. However, long Reed-Solomon codes are difficult to implement and many commun...