Supplement to the paper "Gauss Sums, Jacobi Sums, and $p$-ranks of Cyclic Difference Sets"

Supplement to the paper "Gauss Sums, Jacobi Sums, and p-ranks of Cyclic Difference Sets" by Ronald Evans, Henk Hollmann, Christian Krattenthaler, and Qing Xiang

Below we provide Maple and Mathematica inputs for generating the adjacency matrices which are used in the proofs of Theorems 4.6 and 4.8, and we provide the proof of the fact (mentioned in the Remark on page 30) that the number A_{\sigma+\gamma}(3u) is never a power of 3.

Here is the Maple code (not recommended; this takes really forever ...), and here is the Mathematica code (this is, surprisingly, much faster), for generating the matrices A_{00}, A_{01}, A_{12}, and A_{20} of the proof of Theorem 4.6, and for testing the recurrence (4.8).

Here is the Maple code (not recommended; this takes really forever ...), and here is the Mathematica code (this is, surprisingly, much faster), for generating the matrices A_{00}, A_{01}, A_{12}, A_{23}, A_{34}, and A_{40} of the proof of Theorem 4.8, and for testing the recurrence (4.22).

Here is the proof of the above mentioned fact in the Remark on page 33, together with the computer data on which it is based.