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: A bound on the minimal field size of LRCs, and cyclic MR codes that attain it. (19/3/2023)
- A new journal paper: Perfect codes correcting a single burst of limited-magnitude errors. (21/1/2023)
- A new journal paper: On the reverse-complement string-duplication system. (23/10/2022)
- A new journal paper: Opitmal locally repairable codes: an improved bound and constructions. (14/7/2022)
- Three new conference papers from ISIT 2022. (5/7/2022)
- A new journal paper: Sequence reconstruction for limited-magnitude errors. (18/6/2022)
- A new journal paper: On the generalized covering radii of Reed-Muller codes. (18/6/2022)
- A new journal paper: Improved rank modulation for DNA storage with shotgun sequencing. (20/5/2022)