EAQEC codes from polycyclic codes over the ring R_l

Gokul  Radhakrishnan; Karthick  Gowdhaman; Mahalakshmi Jothi  Ramanujam; Cruz  Mohan; Durairajan  Chinnapillai

doi:10.13069/jacodesmath.v13i2.390

Gokul Radhakrishnan Department of Mathematics, Bharathidasan University, Tiruchirappalli-620 024, Tamil Nadu, India
Karthick Gowdhaman Department of Mathematics, SASTRA Deemed University, Thanjavur-613401, Tamil Nadu, India
Mahalakshmi Jothi Ramanujam Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, India
Cruz Mohan Department of Mathematics, Bishop Heber College, Tiruchirappalli - 620 017, Tamil Nadu, India
Durairajan Chinnapillai Department of Mathematics, Bharathidasan University, Tiruchirappalli - 620 024, Tamil Nadu, India

DOI: https://doi.org/10.13069/jacodesmath.v13i2.390

Keywords: Semi-simple ring, Polycyclic codes, Hamming distances, Gray maps, Annihilator dual codes

Abstract

In this paper, we study polycyclic codes over the ring R_l = F_q[w] / 〈w^l − 1〉 with q = p^k, where k is a positive integer and p is an odd prime. We explore LCD annihilator, self-dual, self-orthogonal codes over R_l and polycyclic codes over R_l. Moreover, we provide a structure of entanglement-assisted quantum error-correcting codes based on the developed polycyclic codes through the inclusion of dual contained conditions. Subsequently, some LCD hull code-derived entanglement-assisted quantum error-correcting code examples are presented.