Mathematics

Turbo code

Block code

Reed–Muller code

Computer science

Theoretical computer science

Decoding methods

Tornado code

Telecommunications

Reed–Solomon error correction

Concatenated error correction code

Arithmetic

IEEE Transactions on Information Theory

In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed–Solomon codes. Whereas Reed–Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless, we show that our construction yields several families of MDS codes. Further, for a large subclass of (MDS) twisted RS codes, we show that the new codes are not generalized RS codes. To achieve this, we use properties of Schur squares of codes as well as an explicit description of the dual of a large subclass of our codes. We conclude the paper with a description of a decoder, that performs very well in practice as shown by extensive simulation results.

Twisted Reed–Solomon Codes