2022/04/02 by Sanjit Bhowmick, Bhowmick, Sanjit, Alexandre Fotue Tabue +3
Computer Science · #51E22 #94B05 #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2204.00905
openalex publication_date 2022/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generalizing the linear complementary duals, the linear complementary pairs and the hull of codes, we introduce the concept of ℓ-dimension linear intersection pairs (ℓ-DLIPs) of codes over a finite commutative ring (R), for some positive integer ℓ. In this paper, we study ℓ-DLIP of codes over R in a very general setting by a uniform method. Besides, we provide a necessary and sufficient condition for the existence of a non-free (or free) ℓ-DLIP of codes over a finite commutative Frobenius ring. In addition, we obtain a generator set of the intersection of two constacyclic codes over a finite chain ring, which helps us to get an important characterization of ℓ-DLIP of constacyclic codes. Finally, the ℓ-DLIP of constacyclic codes over a finite chain ring are used to construct new entanglement-assisted quantum error correcting (EAQEC) codes.