2021/05/02 by Lin Sok, Sok, Lin
Computer Science · #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.2105.00513
openalex publication_date 2021/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that any Hermitian self-orthogonal [n,k,d]q2 code gives rise to an [n,k,d]q2 code with ℓ dimensional Hermitian hull for 0≤ ℓ ≤ k. We present a new method to construct Hermitian self-orthogonal [n,k]q2 codes with large dimensions k>(n+q-1)/(q+1). New families of Hermitian self-orthogonal codes with good parameters are obtained; more precisely those containing almost MDS codes. By applying a puncturing technique to Hermitian self-orthogonal codes, MDS [n,k]q2 linear codes with Hermitian hull having large dimensions k>(n+q-1)/(q+1) are also derived. New families of MDS, almost MDS and optimal codes with arbitrary Hermitian hull dimensions are explicitly constructed from algebraic curves. As an application, we provide entanglement-assisted quantum error correcting codes with new parameters.