Title :
The Algebraic Degree of Perfect Binary Codes
Author_Institution :
CSIRO ICT Centre, Marsfield, NSW
Abstract :
In this communication, we give a complete characterization for the range of the algebraic degree of perfect binary codes. For 1 -perfect binary codes, we show that for any d in the algebraic degree range, there are Vasil´ev codes with algebraic degree d. It is also shown that the algebraic degree of 1-perfect binary codes is independent of the rank and the dimension of the kernel.
Keywords :
algebraic codes; binary codes; Vasil´ev codes; algebraic degree; perfect binary codes; Australia; Binary codes; Boolean functions; Hamming distance; Information theory; Kernel; Polynomials; Affine invariant; algebraic degree; algebraic normal form; leading form; perfect binary code;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2008.929971
