Correction to the paper: Patterson-Wiedemann construction revisited

Abstract

In the paper Patterson-Wiedemann construction revisited by Gangopadhyay et al. (2006), modifying an idempotent function f : GF(2(21)) -> GF(2), which corresponds to a (337, (127)(49))-interleaved sequence whose columns are either all 0's or l's, a balanced function h having Delta(h) < 2 21+1/2- is obtained. In this short note, we find that Delta(f) is computed incorrectly in their paper (leading to Delta(h) not less than 2 21+1/2) and correct their result by disproving the related conjecture for the 21-variable balanced functions. (C) 2015 Elsevier B.V. All rights reserved.