2020/12/31 by Meng Cao, Cao, Meng
Computer Science · #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2012.15691
openalex publication_date 2020/12/31 · openalex created_date 2022/11/06 · openalex updated_date 2026/07/28
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain self-orthogonality over finite fields is an effective way to obtain good q-ary quantum codes of large length. This article has two purposes: the first is to summarize some results of this topic obtained by the author of this article and his cooperators in [10-12]; the second is to add some new results on quasi-orthogonal matrices (resp. quasi-unitary matrices), Euclidean dual-containing (resp. Hermitian dual-containing) matrix-product codes and q-ary quantum codes derived from these matrix-product codes.