Primitive transformation shift registers of order two over fields of\n characteristic two

2016/03/29 by Ambrish Awasthi, Awasthi, Ambrish, R. K. Sharma +1
Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1603.08722

openalex publication_date 2016/03/29 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

We consider the problem of enumeration of primitive TSRs of order n over any\nfinite field. Here we prove the existence of primitive TSRs of order two over\nbinary field extensions. Moreover we give a general search algorithm for\nprimitive TSRs of odd order over any finite field and in particular of order\ntwo over fields of characteristic 2. We also give certain bounds on the number\nof primitive TSRs in special cases and propose a conjecture regarding the\nexistence of certain special type of primitive polynomials, which answers the\nexistence of primitive TSRs of odd order n over Fqm and primitive TSRs of order\ngreater than 3 over binary field extensions..\n

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