Racetrack memory is a new technology, which utilizes magnetic domains along a
nanoscopic wire in order to obtain extremely high storage density. In racetrack memory …

Optimal rank-metric codes in Ferrers diagrams are considered. Such codes consist of
matrices having zeros at certain fixed positions and can be used to construct good codes in …

The rank modulation scheme has been proposed for efficient writing and storing data in
nonvolatile memory storage. Error correction in the rank modulation scheme is done by …

We consider lattice tilings of ℝ n by a shape we call a (k+, k-, n)-quasi-cross. Such lattices
form perfect error-correcting codes which correct a single limited-magnitude error with …

Error-correcting codes were introduced to combat errors in communication channels,
storage devices, and other computerized systems. In each such system, the information may …

A well-known conjecture of Golomb and Welch is that the only nontrivial perfect codes in the
Lee and Manhattan metrics have length two or minimum distance three. This problem and …

A perfect code in a graph Γ=(V, E) is a subset C of V that is an independent set such that
every vertex in V∖ C is adjacent to exactly one vertex in C. A total perfect code in Γ is a …

Since 1968, when the Golomb-Welch conjecture was raised, it has become the main motive
power behind the progress in the area of the perfect Lee codes. Although, there is a vast …

Lee codes have been intensively studied for more than 40 years. Interest in these codes has
been triggered by the Golomb-Welch conjecture on the existence of the perfect error …

Using synthetic DNA for data storage and for physical information encoding in labeling,
tracing, and authentication applications is becoming more feasible as synthesis and reading …