#####
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.