Abstract: The Hellseth-Gong(HG) sequence is a kind of CDMA sequences used in wireless communication systems with ideal autocorrelation. For an odd prime p and integers n,m,d satisfying n=2(2d+1)m , using the theory of quadratic forms and properties of trace transform over finite field, a new unbalanced p -ray CDMA sequence family with large family size and optimal correlation property is constructed based on HG sequences.which means the family has optimal correlation in terms of Welch’s lower bound.Similarly,for an even number n=2(2d+1)m , using the trace transform,a family of balanced p -ray CDMA sequences with large family size has the property of optimal correlation,which is constructed from the unbalanced p-ray CDMA sequence family.It is shown that the two CDMA sequence families have large period and linear span,and are sutable for transmission in wireless communication systems.

Key words: p-ray sequence , optimal correlation, balanced sequence, linear spannel