Estimations of linear characteristics of some classes of functions over Galois rings

O. V. Kamlovskii, R. V. Penzyakov

MIREA — Russian Technological University, Moscow

Abstract: We define linear characteristics of functions over Galois ring. These characteristics show how ”close” functions are to the class of affine functions over the considered ring. We prove the criterion to be a bent function over Galois rings in terms of linear characteristics. We estimate linear characteristics of branching functions and functions from the Eliseev-Maiorana-McFarland class and the Dobbertin class.

Keywords: linear characteristics of functions, Galois rings, additive character sums, bent functions.

UDC: 511.336+519.113.6

Received: 03.07.2025

DOI: 10.4213/dm1880