Constructions of bent functions from two known bent functions

Abstract

A (1, -1)-matrix will be called a bent type matrix if each row and each column are bent sequences. A similar description can be found in Carlisle M. Adams and Stafford E. Tavares, Generating and counting binary sequences, IEEE Trans. Inform. Theory, vol. 36, no. 5, pp. 1170-1173, 1990, in which the authors use the properties of bent type matrices to construct a class of bent functions. In this paper we give a general method to construct bent type matrices and show that the bent sequence obtained from a bent type matrix is a generalized result of the Kronecker product of two known bent sequences. Also using two known bent sequences of length 2 2k\\Gamma2 we can construct 2 k \\Gamma 2 bent sequences of length 2 2k , more than in the ordinary construction, which gives construct 10 bent sequences of length 2 2k from two known bent sequences of length length 2 2k\\Gamma2 . Let V n be the vector space of n tuples of elements from GF (2). Let ff; fi 2 V n . Write ff = (a 1 ; \\Delta ...