We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature employ trace polynomials. The are over \mathbb F ql have redundancy r = n-k ≥ q m , 1 ≤...

The q-ary Reed-Muller codes RMq(u,m) of length n = q are a generalization of Reed-Solomon codes, which use polynomials in m variables to encode messages through functional encoding. Using an idea of reducing the multivariate case to the univariate case, randomized list-decoding algorithms for Reed-Muller codes were given in [1] and [15]. The algorithm in [15] is an improvement of the algorithm ...

Baldi et al. proposed a variant of McEliece’s cryptosystem. The main idea is to replace its permutation matrix by adding to it a rank 1 matrix. The motivation for this change is twofold: it would allow the use of codes that were shown to be insecure in the original McEliece’s cryptosystem, and it would reduce the key size while keeping the same security against generic decoding attacks. The aut...

Codes with traceability properties are used in schemes where the identification of users that illegally redistribute content is required. For any code with traceability properties, the Identifiable Parent Property (c-IPP) seems to be less restrictive than the Traceability (c-TA) property. In this paper, we show that for ReedSolomon codes both properties are in many cases equivalent. More precis...

The purpose of this paper is to demonstrate that a distinguisher of Reed-Solomon codes based on the square code construction leads to the cryptanalysis of several cryptosystems relying on them. These schemes are respectively (i) a homomorphic encryption scheme proposed by Bogdanov and Lee; (ii) a variation of the McEliece cryptosystem proposed by Baldi et al. which firstly uses ReedSolomon code...

In this paper, a serial concatenation scheme and its iterative decoding algorithm between Low Density Parity Check codes (LDPC) and Reed-Solomon codes are proposed. For the decoder, the soft output values delivered by LDPC are used as reliability values to perform the Chase decoding of Reed-Solomon (RS) codes which return soft information to LDPC decoder. This approach presents an option scheme...

In this article we count the number of [n, k] generalized Reed– Solomon (GRS) codes, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of [n, 3] MDS codes with n = 6, 7, 8, 9.

The best known constructions for arrays with low bias are those from 1] and the exponential sum method based on the Weil-Carlitz-Uchiyama bound. They all yield essentially the same parameters. We present new eecient coding-theoretic constructions, which allow far-reaching generalizations and improvements. The classical constructions can be described as making use of Reed-Solomon codes. Our recu...

a method is introduced for efficient encoding and decoding of the Reed-Solomon codes based on the matrix formalism. In this ideology, a method is suggested for vectorization of the Berlekamp-Massey algorithm for detecting and correcting several silent data corruptions. The results of comparison of suggested method with other knows ways of decoding RS codes are presented. This approach requires ...