A large class of MDS linear codes is constructed. These are endowed with an efficient decoding algorithm. Both the definition and design their algorithm only require from Linear Algebra methods, making them fully accessible for everyone. Thus, first part paper develops a direct presentation by means parity-check matrices, rests upon matrix maps manipulations. The somewhat more sophisticated mat...

Up until now, we have seen bounds that tell us good codes should be possible but we didn’t know how to construct such codes explicitly. The binary Reed-Solomon code gave us good rate but poor distance. Intuitively, we should be able to concatenate it with an inner code that would “amplify” its distance. Enumerating and searching codes takes O(2) time, so we can’t just find one good inner code a...

One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized Reed-Solomon codes. We also present some classes of quantum codes from matrix-product codes. It turns out that many of our quantum codes are new in the sense that the ...

This paper presents an algorithmic improvement to Sudan’s list-decoding algorithm for Reed-Solomon codes and its generalization to algebraic-geometric codes from Shokrollahi and Wasserman. Instead of completely factoring the interpolation polynomial over the function field of the curve, we compute sufficiently many coefficients of a Hensel development to reconstruct the functions that correspon...

391 Abstract— Detection and correction of errors in digital data is an important issue for the modern communication systems. Therefore an efficient error control code is needed to protect the digital data. In high speed communication system Reed-Solomon codes are widely used to provide error protection especially against the burst errors. Reed-Solomon codes are cyclic, non-binary codes. In this...

This paper examines a coded Gaussian Minimum Shift Keying (GMSK) system which uses Reed-solomon (RS) codes in Additive White Gaussian Noise channels.The performance of GMSK and RS code combinations is compared with the constraint that the transmission bandwidth is constant. The coding gains were obtained using simulations and the best combination of GMSK and RS codes was found. Keywords—GMSK, R...

395 Abstract—Reed-Solomon Codes are popularly used for error correction in many applications like storage devices (CD, DVD), wireless communications, high speed modems and satellite communications. In this paper, a modified scheme for programmable generator polynomial based Reed-Solomon encoder and decoder has been proposed. The works reported in this paper corrects errors in derived equations ...

AbsrructAn ( n, k, d) linear code over F = GF( q) is said to be ntcrximunt dktunce separable (MDS) if d = n k + 1. It is shown that an (II, k, FI k + 1) generalized Reed-Solomon code such that 2 I k 5 n 1 ((I 1)/2] (k + 3 if q is even) can be extended by one digit while preserving the MDS property if and only if the resulting extended code is also a generalized Reed-Solomon code. It follows tha...

In the present world, communication system which includes wireless, satellite and space communication, reducing error is being critical. During message transferring the data might get corrupted, so high bit error rate of the wireless communication system requires employing to various coding methods for transferring the data. Channel coding for detection and correction of error helps the communi...