Improve the generalized von Neumann inequality for MDS linear forms

Establish a stronger generalized von Neumann inequality for the linear forms of maximum-distance-separable codes and the leakage functions arising in local leakage analysis, with sufficiently improved bounds to yield local leakage resilience over smaller finite fields.

Background

The paper explains that prior higher-order Fourier analyses retain only one small Gowers-norm factor, forcing exponentially large field sizes at constant threshold rate. Nguyen conjectured that a better understanding of the relevant inequality for MDS systems and leakage functions could produce bounds over smaller fields. The present paper instead obtains linearly many Gowers-norm factors, but the quoted conjecture remains an explicitly stated unresolved direction.