Balanced nonbinary sequences with good periodic correlation properties obtained from modified Kumar-Moreno sequences

Kumar and Moreno (see ibid., vol.37, no.3, p.603, 1991) presented a new family of nonbinary sequences which has not only good periodic correlation properties but also the largest family size. First, the unbalanced properties for Kumar-Moreno sequences are pointed out. Second, a new family of balanced nonbinary sequences obtained from modified Kumar-Moreno sequences is proposed, and it is shown that the new family has the same optimal periodic nontrivial correlation as the family of Kumar-Moreno sequences and consists of the balanced nonbinary sequences. It is also shown that the cost of making sequences balanced is a decrease of the family size in addition to the condition that n is an even number. In particular, let the length of Kumar-Moreno sequences and the new sequences be the same and equal to pⁿ-1 with n even, then the family size of the new sequences is p^n/2 which is much smaller than pⁿ, that of Kumar-Moreno sequences