Error-correcting codes from k-resolving sets

Error-correcting codes from k-resolving sets

We demonstrate a construction of error-correcting codes from graphs by means of k-resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the k-metric dimension of grid graphs (i.e. Cartesian products of paths). MSC 2010: 05C12, 94B25 (primary); 05B40, 94B35 (secondary).

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...