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Full-Text Articles in Number Theory
Factors Of Dickson Polynomials Over Finite Fields, Robert W. Fitzgerald, Joseph L. Yucas
Factors Of Dickson Polynomials Over Finite Fields, Robert W. Fitzgerald, Joseph L. Yucas
Articles and Preprints
We give new descriptions of the factors of Dickson polynomials over finite fields.
Highly Degenerate Quadratic Forms Over Finite Fields Of Characteristic 2, Robert W. Fitzgerald
Highly Degenerate Quadratic Forms Over Finite Fields Of Characteristic 2, Robert W. Fitzgerald
Articles and Preprints
Let K/F be an extension of finite fields of characteristic two. We consider quadratic forms written as the trace of xR(x), where R(x) is a linearized polynomial. We show all quadratic forms can be so written, in an essentially unique way. We classify those R, with coefficients 0 or 1, where the form has a codimension 2 radical. This is applied to maximal Artin-Schreier curves and factorizations of linearized polynomials.
Sums Of Gauss Sums And Weights Of Irreducible Codes, Robert W. Fitzgerald, Joseph L. Yucas
Sums Of Gauss Sums And Weights Of Irreducible Codes, Robert W. Fitzgerald, Joseph L. Yucas
Articles and Preprints
We develop a matrix approach to compute a certain sum of Gauss sums which arises in the study of weights of irreducible codes. A lower bound on the minimum weight of certain irreducible codes is given.