@article{article_1654134, title={On the Cyclic and-Constacyclic Codes over the Quaternion Rings and Their Applications}, journal={Journal of Universal Mathematics}, volume={8}, pages={93–103}, year={2025}, DOI={10.33773/jum.1654134}, author={Dertli, Abdullah and Çengellenmiş, Yasemin}, keywords={Kuaternion halkası, kuantum kodlar, devirli kodlar, constacyclic kodlar}, abstract={In this paper, the structures of linear codes over the quaternion rings with coe cient from Zp, Hp = Zp+Zpi+Zpj+Zpk are given, where p is an odd prime, i2 = j2 = k2 = p 1 and ij = (p 1)ji = k. The quaternion rings over Zp decompose into two parts form Zp + iZp(or Zp + jZp or Zp +kZp) with idempotent coe cients, depending on selecting a central orthogonal idempotent pair. The structures of cyclic and-constacyclic codes over Hp are determined, where p 3(mod 4), p is an odd prime, is a unit in Hp and some examples are given. The duals of linear codes over Hp are investigated. The parameters of quantum codes are obtained from cyclic codes and-constacyclic over Hp.}, number={2}, publisher={Gökhan ÇUVALCIOĞLU}