The generalized Wilson theorem we present, based on an algebraic delta function that enables the explicit formulation of operations over finite fields. Matters to be discussed include sums of multinomial coefficients and particularly how classical Wilson’s theorem arose as a particular instance of the result de-rived. The authors established that there exist applications of our approach methods in practically every domain of information security, from secure classification implementation within artificial intelligence systems up to error correcting code design. This mathematical model will enhance robustness in AI systems toward input perturbation when there is limited trust regarding the execution environment. The work is interdisciplinary in nature, combining tools from number theory, coding theory, and algebraic logic, thus offering new perspectives for applications in cryptography, digital testing, and the development of secure computational architectures.