2021/11/12 by Xiang‐dong Hou, Hou, Xiang-dong, Vincenzo Pallozzi Lavorante +1 · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Cryptographic Implementations and Security #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2111.06533
After a brief review of existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bring a PB to its canonical form under equivalence. We then focus on PBs of \Bbb Fq2 of the form Xn(Xd(q-1)+a), where n and d are positive integers and a∈\Bbb Fq2^*. Our contributions include two nonexistence results: (1) If q is even and sufficiently large and aq+1≠ 1, then Xn(X3(q-1)+a) is not a PB of \Bbb Fq2. (2) If 2≤ d| q+1, q is sufficiently large and aq+1≠ 1, then Xn(Xd(q-1)+a) is not a PB of \Bbb Fq2 under certain additional conditions. (1) partially confirms a recent conjecture by Tu et al. (2) is an extension of a previous result with n=1.