Complete classification of repeated-root σ-constacyclic codes of prime power length over Fpm

Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over \({{\mathbb{F}_{p^m}[u]}/{\langle u^3\rangle}}\)

“…where γ is a nonzero element of F p m . In [26], Laaouine et al classified all γ-constacyclic codes of length p s over R.…”

“…Theorem 1 (cf. [26]). The ring R γ is a local finite non chain ring with maximal ideal u, x − γ 0 , where γ 0 ∈ F p m such that γ p s 0 = γ.…”

“…Theorem 2 (cf. [26]). Let C be a γ-constacyclic codes of length p s over R. Then following the same notations as in Theorem 1, we have the following results:…”

“…DNA cyclic codes over F 2 + uF 2 + u 2 F 2 were studied in [25]. In [26], Laaouine et al obtained the structure of all γ-constacyclic codes of length p s over F p m + uF p m + u 2 F p m by classifying them into eight types, where γ is a nonzero element of F p m . The Hamming distances of γ-constacyclic codes of length p s over R have been computed by Dinh et al [27].…”

Hamming Distance of Constacyclic Codes of Length ps Over F pm +uF pm +u²F pm

“…When = 3, in 2015, [35] determined the structure of (δ + αu 2 )-constacyclic codes of length p s over F p m [u]/ u 3 = F p m +uF p m +u 2 F p m . Recently, [23] obtained the structure of all constacyclic codes of length p s over F p m +uF p m +u 2 F p m by classifying them into 8 types. [34] studies the structure of repeated-root constacyclic codes of of any length over F p m + uF p m + u 2 F p m and provided the Hamming distnace of some of them.…”