On a Connection between Ideal Two-level Autocorrelation and Almost Balancedness of $p$-ary Sequences

In this correspondence, for every periodic p−ary sequence satisfying ideal two-level autocorrelation property the existence of an element of the field GF(p) which appears one time less than all the rest that are equally distributed in a period of that sequence, is proved by algebraic method. In addition, it is shown that such a special element might not be only the zero element but as well arbitrary element of that field. Index Terms almost balancedness, ideal two-level autocorrelation property.