The automorphism groups of Reed-Solomon codes

Automorphism 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...

Quantum Reed-Solomon Codes

During the last years it has been shown that computers taking advantage of quantum mechanical phenomena outperform currently used computers. The striking examples are integer factoring in polynomial time (see [8]) and finding pre– images of an n–ary Boolean function (“searching”) in time O( √ 2n) (see [5]). Quantum computers are not only of theoretical nature—there are several suggestions how t...

Parallel Reed-Solomon Codes

The compound and integrated parallel Reed-Solomon (RS) codes for multichannel communication systems are suggested. The matrix model of errors for such codes is investigated. Methods of coding and decoding of parallel RS codes, and also methods of increase of their error correcting capability are developed.

Reed-solomon Group Codes

Notes on Reed-solomon Codes

Reed-Solomon codes are examples of error correcting codes, in which redundant information is added to data so that it can be recovered reliably despite errors in transmission or storage and retrieval. The error correction system used on CD’s and DVD’s is based on a Reed-Solomon code. These codes are also used on satellite links and other communications systems. We will first discuss the general...