Reed-solomon Group Codes
نویسندگان
چکیده
منابع مشابه
A general construction of Reed-Solomon codes based on generalized discrete Fourier transform
In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes enjoy nice algebraic properties just as the classic one.
متن کاملThe Generalized Reed-Muller codes in a modular group algebra
First we study some properties of the modular group algebra Fpr [G] where G is the additive group of a Galois ring of characteristic pr and Fpr is the field of p r elements. Secondly a description of the Generalized Reed-Muller codes over Fpr in Fpr [G] is presented.
متن کاملUpper Bounds on the Number of Codewords of Some Separating Codes
Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study upper bounds for separating codes. First, some new upper bound for restricted separating codes is proposed. Then we illustrate that the Upper Bound Conjecture f...
متن کاملAutomorphism groups of generalized Reed-Solomon codes
We look at AG codes associated to P, re-examining the problem of determining their automorphism groups (originally investigated by Dür in 1987 using combinatorial techniques) using recent methods from algebraic geometry. We classify those finite groups that can arise as the automorphism group of an AG code and give an explicit description of how these groups appear. We give examples of generali...
متن کاملMulti-Dimensional Nonsystematic Reed-Solomon Codes
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.
متن کامل