New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes

Abstract

In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner product. As the computational results, five new binary quantum codes with parameters [[

New Binary Quantum Codes Constructed from Quasi-Cyclic Codes

“…Quantum error-correcting codes (QECCs) play an essential role in safeguarding quantum information from being corrupted by undesirable environmental and operational noise (decoherence). Since the first [ [9,1,3]] 2 QECC was derived by Shor [12] in 1995, many scholars have extensively investigated the construction of QECCs that perform well on quantum error-correction. In [13,14,2,8], the association between QECCs and classical codes with certain self-orthogonal parameters are established.…”

“…Thereby, Ezerman et al [3] employed quantum Construction X to QC codes with large Hermitian hulls and derived a new [[31, 9, 7]] 2 QECC. In addition to that, by studying several classes of QC codes, Lv et al [9,11,10] obtained many binary QECCs with better performance than the best-known ones through symplectic and Hermitian constructions in turn. In [15] and [16], the work of Lv et al were further advanced by Yao et al to determine the selforthogonal conditions for two classes of quasi-twisted codes and constructed two recordbreaking binary QECCs.…”

Extended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codes

“…Then, Ashikhmin et al [2] generalized these results to non-binary case . Afterwards, many good QECCs have been constructed by using classical linear codes over finite fields [1,9,12,16,18,25,27,34,38]. Another important discovery in the quantum errorcorrecting area was the entanglement-assisted quantum codes (EAQECCs, for short).…”

“…In 2019, Ezerman et al [9] employed QC codes with large Hermitian hulls to provide QECCs and gained a record-breaking binary [ [31,9,7]] QECC. In [25,26], we have obtained some good QECCs from one-generator and two-generators QC codes that are symplectic self-orthogonal, respectively. It is well-known that extended constructions of linear error-correcting codes are extremely effective methods to obtain new codes with good performance, such as famous generalized Reed-Muller codes, generalized Reed-Solomon codes and so on.…”

On Steane-enlargement of quantum codes from Cartesian product point sets

“…Traditionally, quantum codes were only studied in the symmetric case, but by now the literature contains a great number of works studying either of the two types of codes. In this work, we only consider symmetric codes, and some recent developments in this field are [7,18,19,21,22,25,31]. In this setting, the code parameters are commonly written in the form [[n, k, d]] q , and we will follow this convention.…”