Generalized Rothaus construction and non-weakly regular bent functions

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• 作者：Wilfried Meidl ^{meidlwilfried@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Bent function ; Non-weakly regular ; Vectorial bent function ; Rothaus construction ; Coulter&ndash ; Matthews
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：141
• 期：Complete
• 页码：78-89
• 全文大小：337 K

文摘

In this article a construction of bent functions from an n  -dimensional vector space 16000182&_mathId=si1.gif&_user=111111111&_pii=S0097316516000182&_rdoc=1&_issn=00973165&md5=1aeecc74c545357eac88544bfe243248" title="Click to view the MathML source">V_n$V_n$ over 16000182&_mathId=si2.gif&_user=111111111&_pii=S0097316516000182&_rdoc=1&_issn=00973165&md5=a210c63de828015042d1123cdc2e5e36" title="Click to view the MathML source">F_p${\mathbb{F}}_p$ to 16000182&_mathId=si2.gif&_user=111111111&_pii=S0097316516000182&_rdoc=1&_issn=00973165&md5=a210c63de828015042d1123cdc2e5e36" title="Click to view the MathML source">F_p${\mathbb{F}}_p$ is presented for arbitrary primes p   and dimensions 16000182&_mathId=si3.gif&_user=111111111&_pii=S0097316516000182&_rdoc=1&_issn=00973165&md5=62a65c30a01af31c653e325c84dd228f" title="Click to view the MathML source">n≥5$n\ge 5$. The construction can be seen as generalization of the Rothaus construction for Boolean bent functions. Since vectorial bent functions are used, we recall some classes of vectorial bent functions and employ them to obtain both, weakly regular and non-weakly regular bent functions. The suggested construction provides the second known procedure to design non-weakly regular bent functions.