Prof. Aiden Bruen’s has recently contributed a paper https://arxiv.org/abs/2102.12692 in which he shows how the Shannon entropy function is expressible as a linear combination of other Shannon entropy functions involving quotients of polynomials in *p, q* * *of degree

*n*for any

*n*>=

*2*.

Chapter 25 of the forthcoming 2nd Edition of the Handbook contains all the background information, additional details, and related material.

*2020 MSC: 94A15 Information theory, 94A17 Measures of information, entropy, 94A60 Cryptography*