Ternary m-sequences with three-valued cross-correlation function: new decimations of Welch and Niho type

We show that the cross correlation between two ternary m-sequences of period 3ⁿ-1 that differ by the decimation d=2·3^m+1, where n=2m+1, takes on three different values. We conjecture the same result for the decimation d=2·3 ^r+1, where n is odd and r is defined by the condition 4r+1≡0 mod n. These two new cases form in a sense ternary counterparts of two previously confirmed binary cases, the conjectures of Welch and Niho (1972)