文摘
In this article a construction of bent functions from an m>n m>-dimensional vector space mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0097316516000182&_mathId=si1.gif&_user=111111111&_pii=S0097316516000182&_rdoc=1&_issn=00973165&md5=1aeecc74c545357eac88544bfe243248" title="Click to view the MathML source">VnmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><msub><mrow><mi>Vmi>mrow><mrow><mi>nmi>mrow>msub>math> over mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0097316516000182&_mathId=si2.gif&_user=111111111&_pii=S0097316516000182&_rdoc=1&_issn=00973165&md5=a210c63de828015042d1123cdc2e5e36" title="Click to view the MathML source">FpmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><msub><mrow><mi mathvariant="double-struck">Fmi>mrow><mrow><mi>pmi>mrow>msub>math> to mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0097316516000182&_mathId=si2.gif&_user=111111111&_pii=S0097316516000182&_rdoc=1&_issn=00973165&md5=a210c63de828015042d1123cdc2e5e36" title="Click to view the MathML source">FpmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><msub><mrow><mi mathvariant="double-struck">Fmi>mrow><mrow><mi>pmi>mrow>msub>math> is presented for arbitrary primes m>p m> and dimensions mmlsi3" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0097316516000182&_mathId=si3.gif&_user=111111111&_pii=S0097316516000182&_rdoc=1&_issn=00973165&md5=62a65c30a01af31c653e325c84dd228f" title="Click to view the MathML source">n≥5mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><mi>nmi><mo>≥mo><mn>5mn>math>. 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.