# American Institute of Mathematical Sciences

August  2020, 14(3): 455-466. doi: 10.3934/amc.2020028

## On polycyclic codes over a finite chain ring

 1 Faculty of Science, University of Yaoundé 1, Yaoundé, Cameroon 2 Institute of Mathematics, University of Valladolid, Edificio LUCIA - Campus Miguel Delibes, Valladolid 47011, Castilla, Spain 3 Department of Mathematics, Western Illinois University, 1 University Circle, Macomb, IL61455, USA

* Corresponding author

Received  November 2018 Published  September 2019

Fund Project: The second author is supported by the Spanish MINECO under Grant MTM2015-65764-C3-1

Galois images of polycyclic codes over a finite chain ring $S$ and their annihilator dual are investigated. The case when a polycyclic code is Galois-disjoint over the ring $S,$ is characterized and, the trace codes and restrictions of free polycyclic codes over $S$ are also determined giving an analogue of Delsarte's theorem relating the trace code and the annihilator dual code.

Citation: Alexandre Fotue-Tabue, Edgar Martínez-Moro, J. Thomas Blackford. On polycyclic codes over a finite chain ring. Advances in Mathematics of Communications, 2020, 14 (3) : 455-466. doi: 10.3934/amc.2020028
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