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MacWilliams duality and a Gleason-type theorem on self-dual bent functions. (English) Zbl 1259.94071
Summary: We prove that the MacWilliams duality holds for bent functions. It enables us to derive the concept of formally self-dual Boolean functions with respect to their near weight enumerators. Using this concept, we prove a Gleason-type theorem for self-dual bent functions. As an application, we provide the total number of (self-dual) bent functions in two and four variables obtained from formally self-dual Boolean functions.

##### MSC:
 94B05 Linear codes, general 06E30 Boolean functions 94A60 Cryptography
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##### References:
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