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We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the 1-error correcting property of fivefold codes in any...

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...

We propose a linear optical scheme to transmit an unknown qubit robustly over bit-flip-error channel. To avoid the technical difficulty of the standard quantum error correction code, our scheme is based on the concept of errorrejection. The whole scheme is based on currently existing technology.

The problem of finding quantum-error-correcting codes is transformed into the problem of finding additive codes over the field GF (4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.

Yaakobi et al. (57) ABSTRACT Preferred embodiments of the invention provide WOM cod ing methods and electronic devices With error correcting codes that provide single, double and triple error correction. Preferred codes of the invention also the following property: if the code corrects tWo/three errors it has tWo/three parts of redundancy bits. For double error correction, if only one part of t...

This paper mainly about the study on one of the widely used error correcting codes that is Low parity check Codes (LDPC). In this paper, the Regular LDPC code has been discussed The LDPC codes explained in this paper is about the Regular Binary LDPC codes or the Gallager. Keywords—LDPC, channel coding.

A c-secure code with -error is one of the fingerprinting codes robust against a collusion attack. The purpose of this study is to construct a new c-secure code which has a shorter code length for a largescale collusion than ever proposed. We call this code a c-secure CRT code. Furthermore, we investigate possible approaches to make this code robust against random-error addition. Two approaches ...

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 ...