  In 1998, Lin presented a conjecture on a class of ternary sequences with
ideal 2-level autocorrelation in his Ph.D thesis. Those sequences have a very
simple structure, i.e., their trace representation has two trace monomial
terms. In this paper, we present a proof for the conjecture. The mathematical
tools employed are the second-order multiplexing decimation-Hadamard transform,
Stickelberger's theorem, the Teichm\"{u}ller character, and combinatorial
techniques for enumerating the Hamming weights of ternary numbers. As a
by-product, we also prove that the Lin conjectured ternary sequences are
Hadamard equivalent to ternary $m$-sequences.
