2015/12/04 by Yonglin Cao, Yuan Cao, Cao, Yonglin +5 · 1 citation
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1512.01406
openalex publication_date 2015/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathbbFpm be a finite field of cardinality pm and R=\mathbbFpm[u]/⟨ u2⟩=\mathbbFpm+u\mathbbFpm (u2=0), where p is a prime and m is a positive integer. For any λ∈ \mathbbFpm×, an explicit representation for all distinct λ-constacyclic codes over R of length psn is given by a canonical form decomposition for each code, where s and n are positive integers satisfying \rm gcd(p,n)=1. For any such code, using its canonical form decomposition the representation for the dual code of the code is provided. Moreover, representations for all distinct negacyclic codes and their dual codes of length psn over R are obtained, and self-duality for these codes are determined. Finally, all distinct self-dual negacyclic codes over \mathbbF5+u\mathbbF5 of length 2⋅ 5s⋅ 3t are listed for any positive integer t.