journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2710 New classes of permutation pentanomials over 𝔽52n Gupta Shalini Department of Mathematics & Statistics, Himachal Pradesh University, Shimla, Himachal Pradesh, 171005, India Vinayak Sagar Department of Mathematics & Statistics, Himachal Pradesh University, Shimla, Himachal Pradesh, 171005, India Singh Manpreet Department of Mathematics & Statistics, Himachal Pradesh University, Shimla, Himachal Pradesh, 171005, India 1 20 05 10 2026

Developing novel classes of permutation polynomials(PPs) has become a prominent focus in recent mathematical research. We introduce new classes of permutation pentanomials defined on 𝔽52n through the strategic selection of coefficients expressed as xr h(xq–1), where q = 5n. Over nine distinct classes are identified, with further generalizations achieved by varying the exponent r.

 Permutation polynomial Permutation pentanomial Finite field access open retracted no