Let m, e be positive integers, pa prime number, F _ p^ m F pm be a finite field of p^ m pm
elements and R= F _ p^ mu/⟨ u^ e ⟩ R= F pm u/⟨ ue⟩ which is a finite chain ring. For any ω …

In this paper, an explicit representation and enumeration for negacyclic codes of length $2^
kn $ over the local non-principal ideal ring $ R=\mathbb {Z} _4+ u\mathbb {Z} _4 $$(u^ 2= 0) …

We explicitly determine generators of cyclic codes over a non-Galois finite chain ring Z p
[u]/< u 3> of length pk, where p is a prime number and k is a positive integer. We completely …

We classify all the cyclic self-dual codes of length p^ k pk over the finite chain ring\mathcal
R:=\mathbb Z_p u/⟨ u^ 3 ⟩ R:= Z pu/⟨ u 3⟩, which is not a Galois ring, where p is a prime …

Let F pm be a finite field of cardinality pm and R 3= F pm [u]< u 3>, where p is a prime, m is a
positive integer and u 3= 0. Laaouine et al.(2021)[7] obtained the torsion code and the …

Let F 2 m be a finite field of cardinality 2 m, R= F 2 m [u]∕< u 4> and n be an odd positive
integer. For any δ, α∈ F 2 m×, ideals of the ring R [x]∕< x 2 n−(δ+ α u 2)> are identified as …

Let $\mathbb {F} _ {p^ m} $ be a finite field of $ p^ m $ elements, where $ p $ is a prime
number and $ m $ is a positive integer. Let $ e\geq 2$ be an integer and set $ R=\mathbb {F} …

Cyclic codes play a very important role in the history of coding theory since they have good
algebraic structures that can be widely used in coding and decoding. However, generators …

Let R be a finite commutative chain ring and γ be a fixed generator of the maximal ideal of R.
For any unit w in R,(1+ w γ)-constacyclic codes over R as a generalization of negacyclic …

Abstract Let F _ 2^ m F 2 m be a finite field of 2^ m 2 m elements and denote R= F _ 2^ mu/⟨
u^ k ⟩ R= F 2 mu/⟨ uk⟩= F _ 2^ m+ u F _ 2^ m+ ⋯+ u^ k-1 F _ 2^ m= F 2 m+ u F 2 m+⋯+ uk …