We report on some initial results of a brute-force search for determining the maximum correlation between degree-d polynomials modulo p and the n-bit mod q function. For various settings of the parameters ndp and q, our results indicate that symmetric polynomials yield the maximum correlation. This contrasts with the previously-analyzed settings of parameters, where non-symmetric polynomials yield the maximum correlation. We also prove new properties of maximum-correlation polynomials, and use those to obtain a new setting of parameters where those polynomials are not symmetric.
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