2021/01/16 by Lin Sok, Sok, Lin · 6 citations
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum-Dot Cellular Automata #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.2101.06461
13 pages
arxiv created 2021/01/16 · openalex publication_date 2021/01/16 · arxiv updated 2021/01/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The Euclidean hull of a linear code C is the intersection of C with its Euclidean dual C^⊥. The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the automorphism group of a linear code and checking permutation equivalence of two linear codes. The Euclidean hull of a linear code has been applied to the so-called entanglement-assisted quantum error-correcting codes (EAQECCs) via classical error-correcting codes. In this paper, we consider linear codes with one-dimensional Euclidean hull from algebraic geometry codes. Several classes of optimal linear codes with one-dimensional Euclidean hull are constructed. Some new EAQECCs are presented.