2025/07/01 by Bartoli, Daniele, Borello, Martino, Marino, Giuseppe +1
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2507.00569
In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecting codes in the Hamming metric. A rank-metric code is said to be intersecting if any two nonzero codewords have supports intersecting non trivially. We explore this class from both a coding-theoretic and geometric perspective, highlighting its relationship with minimal codes, MRD codes, and Hamming-metric intersecting codes. We derive structural properties, sufficient conditions based on minimum distance, and geometric characterizations in terms of 2-spannable q-systems. We establish upper and lower bounds on code parameters and show some constructions, which leave a range of unexplored parameters. Finally, we connect rank-intersecting codes to other combinatorial structures such as (2,1)-separating systems and frameproof codes.