Correction to the paper: Patterson-Wiedemann construction revisited

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• 作者：Selç ; uk Kavut ^{skavut@balikesir.edu.tr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Autocorrelation ; Nonlinearity ; PW type functions
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：31 March 2016
• 年：2016
• 卷：202
• 期：Complete
• 页码：185-187
• 全文大小：320 K

文摘

In the paper Patterson–Wiedemann construction revisited   by Gangopadhyay et al. (2006), modifying an idempotent function $f:GF\left(2^{21}\right)\to GF\left(2\right)$, which corresponds to a (337,(127)(49))$(337,\left(127\right)\left(49\right))$-interleaved sequence whose columns are either all 0’s or 1’s, a balanced function h$h$ having ${\Delta }_h<2^{\frac{21+1}{2}}$ is obtained. In this short note, we find that dad14fb6318" title="Click to view the MathML source">Δ_f${\Delta }_f$ is computed incorrectly in their paper (leading to ${\Delta }_h\nless 2^{\frac{21+1}{2}}$) and correct their result by disproving the related conjecture for the 21-variable balanced functions.