1976/05/01 by Fred G. Gustavson, F. G. Gustavson · 1 citation
Computer Science · Mathematics · #Algorithm #Algorithms and Data Compression #Arithmetic #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics #Computer science #Discrete mathematics #Distribution (mathematics) #Field (mathematics) #Finite field #Linear feedback shift register #Mathematics #Multiplication (music) #Register (sociolinguistics) #Shift register #String (physics)
paper · doi:10.1147/rd.203.0204
crossref issued 1976/05/01 · crossref published 1976/05/01 · crossref published-print 1976/05/01 · openalex publication_date 1976/05/01 · crossref created 2010/04/05 · crossref deposited 2017/11/13 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31
An analysis of the Berlekamp-Massey Linear Feedback Shift-Register (LFSR) Synthesis Algorithm is provided which shows that an input string of length n requires O(n2) multiplication/addition operations in the underlying field of definition. We also derive the length distribution for digit strings of length n. Results show that, on the average, the encoded length is no greater than n + 1 Furthermore, we exhibit a connection between step 1 of the Ling-Palermo algorithm and the LFSR Algorithm, and the LFSR Algorithm turns out to be computationally superior.