Let C be a cyclic code of length p s over R 3 . Then the following code over F p m is called a torsion code with i = 0 , 1 , 2 : Tor i ( C ) = μ ( ( C : R 3 u i ) ...

Finally, by using a one-to-one correspondence between cyclic and alpha-constacyclic codes of length psover F-pm[u]/< u(3)>, we generalize these results to alpha ...

In this paper, we determine the dual codes of cyclic codes of length p s over R 3 = F p m [ u ] 〈 u 3 〉 , where p is a prime number and u 3 = 0 .

Sep 24, 2024 · In this study, we investigate σ-constacyclic codes of length ps over R, that is, ideals of the ring R[x]∕〈xps−σ〉, where σ is a nonzero element ...

Mar 15, 2023 · For a unit λ of R, the λ-constacyclic (λ-twisted) shift τλ on Rn is the shift τλ(x0,x1,...,xn−1) = (λxn−1,x0,x1,...,xn−2), and a code C is said ...

Jul 12, 2024 · u2Fpm , where u3 = 0 and s is a positive integer. If the unit α ∈ Fpm is a square, α = δ2, each α-constacyclic code of length 4ps is ...

Oct 22, 2024 · We show that when p is odd, there is no self-dual (δ+αu2)-constacyclic code of length pk over R and also in the case where p=2, self-dual codes ...

The list of (left and right) α-constacyclic codes of length ps over R is provided where θ(α)=α . The self-dual α-constacyclic codes are given. In addition, we ...

Construction of new quantum codes derived from constacyclic codes over ${\mathbb {F}}_{q^2}+u{\mathbb {F}}_{q^2}+\cdots +u^{r-1}{\mathbb {F}}_{q^2}$.

Oct 18, 2021 · In this paper, we determine the third torsional degrees for all different types of repeated-root cyclic codes over R = Fpm [u]/hu4i of length n ...