Séminaire Lotharingien de Combinatoire, B19e (1988).
[Formerly: Publ. I.R.M.A. Strasbourg, 1988, 361/S-19, p. 126.]

Arne Dür

Über die kanonische Form binärer Formen

Abstract. According to Sylvester, in general, a binary form P of degree n with complex coefficients can be written as a sum of at most (n/2+1) n-th powers of linear forms. Such a representation of minimal length is called a canonical form of P. Algorithms for the computation of a canonical form were already given by Sylvester and Gundelfinger. More efficiently, however, is an extended form of the Berlekamp algorithm for the decoding of Reed-Solomon codes, due to the author [Discrete Math. 90 (1991), 21-40].

The paper has been finally published under the title "On computing the canonical form for a binary form of odd degree" in J. Symbolic Comput. 8 (1989), 327-333.