부산대학교 도서관

Let $ X \in (\Bbb F_p)^n $ be a vector with independent random coordinates taking values in a finite field. The paper under review derives a bound on the total variation distance of $ X $ from the uniform distribution in the binary case $ p=2 $, expressed in terms of the sum of biases of individual bits. This bound is then generalized to the product $ GX $ in place of $ X $, where $ G $ is the generator matrix of a linear code over $ \Bbb F_p = \Bbb F_2 $, and subsequently extended to the case of a general $ p $. A unified treatment is given, based on the Walsh-Hadamard transform and the number theoretic transform.