Constacyclic Codes over Group Ring (Zq[v])/G

Subject Areas : Applied Mathematics

Alireza Soleimani ¹ (Faculty of Mathematics, Tarbiat Modares University, Tehran, Iran)

Received: 2018-07-27 Accepted : 2019-03-04 Published : 2021-05-01

Keywords: " group ring", "code", "constacyclic codes", "ring",

Abstract :

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum information. The construction of quantum codes via classical codes over 2 F was first introduced by Calderbank and Shor [4] and Steane [13] in 1996. This method, known as CSS construction, has received a lot of attention and it has allowed to find many good quantum stabilizer codes. Later, construction of quantum codes over larger alphabets from classical linear codes over q F has shown by Ketkar et al. in [10]. One direction of the main research in quantum error correction codes is constructing quantum codes that have large minimum distances [9] for a given size and length. In [14], based on classical quaternary constacyclic linear codes, some parameters for quantum codes are obtained. In [8, 9], respectively based on classical negacyclic and constacyclic linear codes some parameters for quantum MDS codes are presented. In this work, we determine self-dual and self-orthogonal codes arising from constacyclic codes over the group ring(Zq[v]/G