2016/08/24 by Yongsheng Tang, Shixin Zhu, Tang, Yongsheng +5
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.1608.06674
openalex publication_date 2016/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R=\mathbbF2m+u\mathbbF2m+⋯+uk\mathbbF2m , where \mathbbF2m is a finite field with 2m elements, m is a positive integer, u is an indeterminate with uk+1=0. In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over R. A new Gray map over R is defined and a sufficient and necessary condition for the existence of dual-containing cyclic codes over R is given. A new family of 2m-ary quantum codes is obtained via the Gray map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R. Furthermore, a new family of binary quantum codes is obtained via the Gray map, the trace map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R.