Erzincan Üniversitesi Erzincan University Fen Bilimleri Enstitüsü Dergisi Journal of Science and Technology 2022 15(1), 46-55 2022 15(1), 46-55 ISSN: 1307-9085, e-ISSN: 2149-4584 DOI: 10.18185/erzifbed.911472 Araştırma Makalesi Research Article *Corresponding Author: ceremnurtetik@gmail.com 46 Quantum Codes from ( − − )-Constacyclic Codes over the + + + + Ceremnur TETIK 1* , Abdullah DERTLI 1 1 Department of Mathematics, Ondokuz Mayıs University, Samsun, Turkey Geliş / Received: 07/04/2021, Kabul / Accepted: 21/12/2021 Abstract In this paper, we give construction of quantum codes over from (1 − 2 − 2) - constacyclic codes over the + + + + , where 2 = , 2 = , 2 = , = , = = = = 0, = , is a positive integer and is an odd prime. We determine the parameters of quantum error correcting codes which constructed from (1 − 2 − 2) - constacyclic codes over the + + + + . Keywords: quantum code, constacyclic code, Gray map + + + + Halkası Üzerindeki ( − − ) –Sabit Devirli Kodlardan Elde Edilen Kuantum Kodlar Öz Bu çalışmada, 2 = , 2 = , 2 = , = , = = = = 0, = , pozitif tam sayı ve tek asal sayı olmak üzere + + + + halkası üzerindeki (1 − 2 − 2)-sabit devirli kodlardan üzerindeki kuantum kodların inşası verilmiştir. Ayrıca, + + + + halkası üzerindeki (1 − 2 − 2) –sabit devirli kodlardan elde edilen hata düzeltici kuantum kodların parametreleri belirlenmiştir. Anahtar Kelimeler: kuantum kod, sabit devirli kod, Gray dönüşümü 1. Introduction At the beginning of the twentieth century, people believed that Newton and Maxwell’s laws of physics were true. By the 1930’s, however, it had become apparent that these classical theories faced serious problems in trying to account for the observed results of certain experiments. As a result, a new mathematical framework for physics called quantum mechanics was formulated, and new theories of physics called quantum physics were developed in this framework (Kaye et al., 2006).