  A pseudorandom number generator is widely used in cryptography. A
cryptographic pseudorandom number generator is required to generate
pseudorandom numbers which have good statistical properties as well as
unpredictability. An m-sequence is a linear feedback shift register sequence
with maximal period over a finite field. M-sequences have good statistical
properties, however we must nonlinearize m-sequences for cryptographic
purposes. A geometric sequence is a binary sequence given by applying a
nonlinear feedforward function to an m-sequence. Nogami, Tada and Uehara
proposed a geometric sequence whose nonlinear feedforward function is given by
the Legendre symbol. They showed the geometric sequences have good properties
for the period, periodic autocorrelation and linear complexity. However, the
geometric sequences do not have the balance property. In this paper, we
introduce geometric sequences of two types and show some properties of
interleaved sequences of the geometric sequences of two types. These
interleaved sequences have the balance property and double the period of the
geometric sequences by the interleaved structure. Moreover, we show correlation
properties and linear complexity of the interleaved sequences. A key of our
observation is that the second type geometric sequence is the complement of the
left shift of the first type geometric sequence by half-period positions.
