Projective Quotient Polynomials and Kernel-Weight Layers over Finite Fields Calculations related to Question 2 of Beierle
Year: 2026
Type: preprint
Abstract: Let L and M be q-polynomials on Fqn , where q is an arbitrary prime power. We study therelationship between their quotient-image sets and the dimensions of the kernels of L − aXand M − aX. A projective product records the integer multiplicities of the quotient values.Its Moore-determinant form yields principal-minor coefficients with Frobenius recurrences.These relations, together with Newton’s identities in characteristic p, determine the coefficientsfrom the quotient-image set and in turn determine each kernel dimension. The associateddifferential-spectrum calculation for x 7 → xL(x) is included.
Author: Berg, Chea
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225629374
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