Title :
The algebraic degree of 1-perfect binary codes and a relation with the code characters
Author_Institution :
CSIRO ICT Centre, Marsfield, NSW
Abstract :
We give a complete characterization for the range of the algebraic degree of 1-perfect binary codes. We show that the algebraic degree range is a compact interval, and that the Vasil´ev construction produces perfect with algebraic degrees covering the entire range. We also hint at a link between the algebraic degree of a perfect binary code and the coefficients of the code character.
Keywords :
algebraic codes; binary codes; 1-perfect binary code character; Vasilev construction; algebraic degree; Arithmetic; Australia; Binary codes; Boolean functions; Polynomials;
Conference_Titel :
Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Conference_Location :
Toronto, ON
Print_ISBN :
978-1-4244-2256-2
Electronic_ISBN :
978-1-4244-2257-9
DOI :
10.1109/ISIT.2008.4595061
