DocumentCode
3559066
Title
The Algebraic Degree of Perfect Binary Codes
Author
Popescu, Dan C.
Author_Institution
CSIRO ICT Centre, Marsfield, NSW
Volume
54
Issue
11
fYear
2008
Firstpage
5198
Lastpage
5202
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;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2008.929971
Filename
4655464
Link To Document