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All α+uβ-constacyclic codes of length nps over \mathbbFpm+u\mathbbFpm

2016/06/21 by Wei Zhao, Xilin Tang, Zhao, Wei +3
Computer Science · #11T71 #94B05 #94B15 #Cellular Automata and Applications #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.1606.06428

openalex publication_date 2016/06/21 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28

Abstract

Let \mathbbFpm be a finite field with cardinality pm and R=\mathbbFpm+u\mathbbFpm with u2=0. We aim to determine all α+uβ-constacyclic codes of length nps over R, where α,β∈\mathbbFpm*, n, s∈ℕ+ and gcd(n,p)=1. Let α0∈\mathbbFpm* and α0^ps=α. The residue ring R[x]/⟨ x^nps-α-uβ⟩ is a chain ring with the maximal ideal ⟨ xn0⟩ in the case that xn0 is irreducible in \mathbbFpm[x]. If xn0 is reducible in \mathbbFpm[x], we give the explicit expressions of the ideals of R[x]/⟨ x^nps-α-uβ⟩. Besides, the number of codewords and the dual code of every α+uβ-constacyclic code are provided.

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