2013/06/20 by Zhixiong Chen
Computer Science · Engineering · Mathematics · #Analytic Number Theory Research #Arithmetic #Binary number #Binary quadratic form #Coding theory and cryptography #Combinatorics #Coset #Discrete mathematics #Fermat number #Fermat's Last Theorem #Legendre symbol #Mathematics #Modulo #Prime (order theory) #Quotient #TRACE (psycholinguistics) #Wieferich prime #cs.CR #graph theory and CDMA systems #math.NT #msc:65C10 #msc:94A55 #msc:94A60
paper · pdf · doi:10.1007/s11432-014-5092-x
14 pages, no figures
arxiv created 2013/06/20 · openalex publication_date 2014/03/20 · arxiv updated 2016/03/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We describe the trace representations of two families of binary sequences derived from Fermat quotients modulo an odd prime p (one is the binary threshold sequences, the other is the Legendre-Fermat quotient sequences) via determining the defining pairs of all binary characteristic sequences of cosets, which coincide with the sets of pre-images modulo p2 of each fixed value of Fermat quotients. From the defining pairs, we can obtain an earlier result of linear complexity for the binary threshold sequences and a new result of linear complexity for the Legendre-Fermat quotient sequences under the assumption of 2p-1\not≡ 1 \bmod p2.