11 papers
Covering Sequences and Covering-Sequences Codes
Tuvi Etzion
The paper studies cyclic sequences whose overlapping n‑tuples form codes with a given covering radius, and shows how Hamming codes can be used to construct short covering sequences…
Optimal Non-Binary Single-Track Gray Code
Tuvi Etzion
The paper proves the existence of non‑binary single‑track Gray codes of certain lengths over prime alphabets, showing constructions for p=3 and p=5 and providing conditions for lar…
Binary and Non-Binary Self-Dual Sequences and Maximum Period Single-Track Gray Codes
Tuvi Etzion
Binary self-dual sequences have been considered and analyzed throughout the years, and they have been used for various applications. Motivated by a construction for single-track Gr…
Closed Expressions for the Weight Distributions of Codes Associated with Perfect Codes
Tuvi Etzion, Denis Krotov, Minjia Shi +1
Perfect codes are arguably the most fascinating structures in combinatorial coding theory, and their classification and weight distribution are of considerable interest. This class…
One-factorizations of complete multipartite graphs with distance constraints
Yuli Tan, Junling Zhou, Tuvi Etzion
The present paper considers multipartite graphs from the perspective of design theory and coding theory. A one-factor of the complete multipartite graph (with $…
New Nonuniform Group Divisible Designs and Mixed Steiner Systems
Tuvi Etzion, Yuli Tan, Junling Zhou
This paper considers two closely related concepts, mixed Steiner system and nonuniform group divisible design (GDD). The distinction between the two concepts is the minimum Hamming…