Linearised polynomial

2020 Mathematics Subject Classification: Primary: 12E10 [MSN][ZBL]

A polynomial over a field of characteristic $p \ne 0$ in which all monomials have exponents which are powers of $p$: $$ L(X) = \sum_{i=0}^d a_i X^{p^i} \ . $$ Such polynomials are additive: $L(x+y) = L(x) + L(y)$.