On the Cyclic and-Constacyclic Codes over the Quaternion Rings and Their Applications

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Journal of Universal Mathematics
Cilt: 8 Sayı: 2
On the Cyclic and-Constacyclic Codes over the Quaternion Rings and Their Applications

On the Cyclic and-Constacyclic Codes over the Quaternion Rings and Their Applications

Authors : Abdullah Dertli, Yasemin Çengellenmiş

Pages : 93-103

Doi:10.33773/jum.1654134

View : 31 | Download : 24

Publication Date : 2025-10-19

Article Type : Research Paper

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.
Keywords : Kuaternion halkası, kuantum kodlar, devirli kodlar, constacyclic kodlar

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