Retraction Note to: On the Minimum the Sum-of-Squares Indicator of a Balanced Boolean Function

Retraction Note to: Chapter “On the Minimum the Sum-of-Squares Indicator of a Balanced Boolean Function” in: Q. Chen et al. (Eds.): Communications and Networking, LNICST 210, https://doi.org/10.1007/978-3-319-66628-0_30

The authors are retracting this article [1] because following its publication a number of errors affecting the validity of the results have come to light.

Specifically

1) The result of Theorem 1 is error. See Page 317.

2) The analysis of Remark 1 is not correct, we cannot obtain the following fact: See Page 320 in Remark 1.

“It is because $wt(f_{1} f_{2}) = 2^{n-3}$ or $2^{n-3} - 1$. It implies that $wt(f_{1}) >= 2^{n-3} - 1$ and $wt(f_{2}) >= 2^{n-3} - 1$”. This fact is error, Thus Corollary 1 is not correct.

3) The result of Corollary 1 is error. See Page 320.

[1] https://doi.org/10.1007/978-3-319-66628-0_30

All authors agree to this retraction.