Quantum codes from codes over Gaussian integers with respect to the Mannheim metric

Abstract

In this paper, some nonbinary quantum codes using classical codes over Gaussian integers are obtained. Also, some of our quantum codes are better than or comparable with those known before, (for instance $[[8,2,5]]_{4+i}$).

Quantum codes do not fix isotropic errors

“…There are many works related to the control of quantum computing errors, in addition to those already mentioned above. General studies and surveys on the subject [20,21,22,23,24,25,26,27], about the quantum computation threshold theorem [28,29,30,31], quantum error correction codes [32,33,34,35], concatenated quantum error correction codes [36,37] and articles related to topological quantum codes [38,39]. Lately, quantum computing error control has focused on both coherent errors [40,41] and cross-talk errors [42,43].…”

Quantum Codes Obtained through Constacyclic Codes over Z3 + νZ3 + ωZ3 + νωZ3

“…Some non binary quantum codes are described using classical codes via Gaussian integers by Ozen et. al [11]. Guenda et.…”

“…In 2016, Ozen et al [12] examined several ternary quantum codes from the cyclic codes over F 3 + uF 3 + vF 3 + uvF 3 . Very recently, several researchers established a number of new quantum codes via F p from the classical cyclic and constacyclic codes to which we refer [2,6,[9][10][11]15]. Also, Singh and Mor [16] constructed quantum codes over the finite non-chain ring = Z p + νZ p where ν 2 = ν in 2021.…”