Consider the set of polynomials of degree at most $n$ over a finite field $k_q$ with $q$ elements where $q$ is prime: $$ P_{n,q} = \left\{ x + c_2 x^2 + \cdots + c_n x^n:\ c_i \in k_q \right\}. $$ It turns out that this set forms a group under composition of polynomials modulo $x^{n+1}$. Could you please tell, is it something well-known, and if it is so, could you please provide any references?
2026-04-07 19:30:29.1775590229
Composition of polynomials over finite fields
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