On polycyclic linear and additive codes associated to a trinomial over a finite chain ring
Abstract
In this paper, we investigate polycyclic codes associated with a trinomial of arbitrary degree n over a finite chain ring R. We extend the concepts of n -isometry and n -equivalence known for constacyclic codes to this class of codes, providing a broader framework for their structural analysis. We describe the classes of n-equivalence and compute their number, significantly reducing the study of trinomial codes over R. Additionally, we examine the special case of trinomials of the form xn - a1x - a0 ∈ R[x] and analyze their implications. Finally, we consider the extension of our results to certain trinomial additive codes over R.
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