Error-correcting codes from graphs

Quantum error-correcting codes associated with graphs

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...

Synchronizable Error-Correcting Codes

A new technique for correcting synchronization errors in the transmission of discrete-symbol information is developed. The technique can be applied to any t-additive-error-correcting Bose-Chaudhuri-Hocquenghem code, to provide protection against synchronization errors. The synchronization error is corrected at the first complete received word after the word containing the synchronization error,...

Parallel error correcting codes

Constructing Quantum Error-Correcting Codes for p-State Systems from Classical Error-Correcting Codes∗

Quantum error-correcting codes have attracted much attention. Among many research articles, the most general and systematic construction is the so called stabilizer code construction [6] or additive code construction [2], which constructs a quantum error-correcting code as an eigenspace of an Abelian subgroup S of the error group. Thereafter Calderbank et al. [3] proposed a construction of S fr...

Error-Correcting Codes Derived from Combinatorial Games

The losing positions of certain combinatorial games constitute linear error-detecting and -correcting codes. We show that a large class of games, which can be cast in the form of annihilation games, provides a potentially polynomial method for computing codes (anncodes). We also give a short proof of the basic properties of the previously known lexicodes, which were defined by means of an expon...