2016/07/05 by Reza Dastbasteh, Dastbasteh, Reza, Seyyed Hamed Mousavi +3
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Mathematics #Rings and Algebras (math.RA) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1607.01368
openalex publication_date 2016/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study cyclic codes with arbitrary length over Fp+vFp where theta(v)=av, a in Fp and v2=0. We characterize all existing codes in case of O(theta)|n by using certain projections from (Fp+vFp)[x;theta] to Fp[x]. We provide an explicit expression for the ensemble of all possible codes. We also prove useful properties of these codes in the case where O(theta)|n does not hold. We provide results and examples to illustrate how the codes are constructed and how their encoding and decoding are realized.