1 Correction to: Des. Codes Cryptogr. https://doi.org/10.1007/s10623-018-0572-4

The original version of this article contains an error. The presentation of Eq. (14) and an expression in Lemma 4 are incorrect. The correct version is given below.

On Section 2, New bound on FH sequences, the Eq. (14) should be

$$\begin{aligned} f(\hbox {gcd}(H_{m}+1,N))= & {} \sum _{d|\, {\mathrm{gcd}}(H_{m}+1,N)} g(d) = \sum _{d|\, {\mathrm{gcd}}(H_{m}+1,N)} \sum _{d^{\prime }|\, d} \mu (d^{\prime })f\left( \frac{d}{d^{\prime }}\right) \nonumber \\= & {} \sum _{\begin{array}{c} d|\, {\mathrm{gcd}}(H_{m}+1,N),\\ d\ne {\mathrm{gcd}}(H_{m}+1,N) \end{array}} \sum _{d^{\prime }|\, d} \mu (d^{\prime })f\left( \frac{d}{d^{\prime }}\right) \nonumber \\&+ \sum _{d^{\prime }|\, {\mathrm{gcd}}(H_{m}+1,N)} \mu (d^{\prime })f\left( \frac{\hbox {gcd}(H_{m}+1,N)}{d^{\prime }}\right) . \end{aligned}$$
(14)

In other words,

$$\begin{aligned} d|\, \hbox {gcd}(H_{m}+1,N), \mathop {\mathop {\mathop {\sum }\limits _{ {\textit{sum}}}}\limits _{d|\, {gcd}(H_{m}+1,N)}}\limits _{{d6={gcd}(H_{m}+1,N)}} d\ne \hbox {gcd}(H_{m}+1,N) \end{aligned}$$

should be rewritten as

$$\begin{aligned} \sum _{\begin{array}{c} d|\, {\mathrm{gcd}}(H_{m}+1,N),\\ d\ne {\mathrm{gcd}}(H_{m}+1,N) \end{array}} \end{aligned}$$

On proof of Lemma 4, “Let \(\bar{n}\) is” should be “Let \(\bar{n}\) be”.

The original article has been corrected.