A counterexample concerning the 3-error linear complexity of 2n-periodic binary sequences

In this article, we present a counterexample to Theorem 4.2 and Theorem 5.2 by Kavuluru (Des Codes Cryptogr 53:75–97, 2009). We conclude that the counting functions for the number of 2n-periodic binary sequences with fixed 3-error linear complexity by Kavuluru are not correct.