The Perfect Cut
Cutting a variant of Sierpinski's triangle (the residues of Pascal's triangle modulo a prime) helps in proving the non-existence of perfect constant-weight codes. Read the full paper.
Constrained Relations
Using networks of relations, an exact solution for the capacity of a two-dimensional constrained system is found (also providing a new exactly-solvable model in statistical mechanics). Read the full paper.
All Bunched Up
A set of points in the 3-dimensional grid, no three too far apart, forms an optimal anticode, and induces lower bounds on the parameters of interleaving schemes combatting error bursts. Read the full paper.
Q*bert Qubes
Long cycles on a hyperplane, reminiscent of the game Q*bert, form asymptotically-optimal constant-weight Gray codes for local-rank modulation, designed for the next generation of flash-memory cells. Read the full paper.
Celtic Knots
When constructing error-correcting codes for DNA storage in living organisms, DNA sequences without repetitions are obtained by paths in a graph resembling a celtic knot. Read the full paper.
Recent News
- A new journal paper: Storage codes on coset graphs with asymptotically unit rate. (15/11/2024)
- A new journal paper: Reconstruction from noisy substrings. (27/10/2024)
- A new journal paper: On duplication-free codes for disjoint or equal-length errors. (18/9/2024)
- A new journal paper: Error correction for DNA storage. (29/8/2024)
- A new journal paper: Bounds on the minimum field size of network MDS codes. (17/7/2024)
- A new conference paper from DRCN won the Best Paper Award! (27/5/2024)
- A new journal paper: Quantized-Constraint Concatenation and the Covering Radius of Constrained Systems. (24/5/2024)