Constacyclic codes of length 2p over Fpm+uFp

Abstract

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Constacyclic codes of length <inline-formula><tex-math id="M1">\begin{document}$np^s$\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M2">\begin{document}$\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$\end{document}</tex-math></inline-formula>

“…Particularly, we present all distinct self-dual negacyclic codes over F 5 + uF 5 of length 2 • 3 t • 5 s for any positive integer t in Section 6. Finally, in Section 7 we obtain conclusions for the special cases of n = 1, 2, 4 which are match known results in [7]- [12].…”

“…There were a lot of literatures on linear codes, cyclic codes and constacyclic codes of length N over rings F p m + uF p m (u 2 = 0) for various prime p and positive integers m and some positive integer N . For example, [1], [2], [4], [7]- [14], [16], [17] and [20]. The classification of codes plays an important role in studying their structures and encoders.…”

“…Dinh et al [10] studied negacyclic codes of length 2p s over the ring F p m + uF p m . Chen et al [7] investigated constacyclic codes of length 2p s over F p m + uF p m . Recently, Dinh et al [11] [12] studied constacyclic codes of length 4p s over F p m + uF p m .…”

“…From now on, let n, s be arbitrary positive integers satisfying gcd(p, n) = 1, and λ be an arbitrary nonzero element of F p m . In this paper, by use of basic theory for linear codes over finite chain rings of length 2, we provide a new way different from the methods used in [7]- [13] to determine precisely the algebraic structures, the generators and enumeration of λ-constacyclic codes over F p m + uF p m of length np s . Specifically, we will address the following questions:…”

RT distance and weight distributions of Type 1 constacyclic codes of length 4ps over Fpm[u]

“…Moreover, in 2015, Dinh et al [25] studied negacyclic codes of length 2p s over the ring F p m + uF p m . Recently, Chen et al [12] determined the algebraic structures of all λ -constacyclic codes of length 2p s over the finite commutative chain ring F p m + uF p m and provided the number of codewords and the dual of every λ -constacyclic code. As a generalization of finite chain rings F p m + uF p m (u 2 = 0) , finite chain rings of the form R a = F p m [u] ⟨u a ⟩ = F p m + uF p m + · · · + u a−1 F p m (u a = 0) have been developed as code alphabet as well.…”