2016/12/21 by Giuliano G. La Guardia, La Guardia, Giuliano Gadioli, Francisco Revson F. Pereira +1
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.1612.07150
openalex publication_date 2016/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we construct several new families of quantum codes with good and asymptotically good parameters. These new quantum codes are derived from (classical) algebraic geometry (AG) codes by applying the Calderbank-Shor-Steane (CSS) construction. Many of these codes have large minimum distances when compared with its code length and they have relatively small Singleton defect. For example, we construct a family [[46; 2(t2 - t1); d]]25 of quantum codes, where t1, t2 are positive integers such that 1 < t1 < t2 < 23 and d >= min 46 - 2t2, 2t1-2, of length n = 46, with minimum distance in the range 2 =< d =< 20, having Singleton defect four. Additionally, by utilizing t-point AG codes, with t >= 2, we show how to obtain sequences of asymptotically good quantum codes.