Maximum Codes with the Identifiable Parent Property

Graph theory;IPP codes

Jiang, Wen ; Mathematics

University:Georgia Institute of Technology

Department:Mathematics

关键词: Graph theory;    IPP codes;   

Others  :  https://smartech.gatech.edu/bitstream/1853/14072/1/jiang_wen_200612.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

We study codes that have identifiable parent property. Such codes are called IPP codes. Research on IPP codes is motivated by design ofschemes that protect against piracy of digital products. Construction and decoding of maximum IPP codes have been studied in rich literature. General bounds on F(n,q), the maximum size of IPPcodes of length n over an alphabet with qelements, have been obtained through the use of techniques from graph theory and combinatorialdesign. Improved bounds on F(3,q) and F(4,q) are obtained. Probabilistic techniques are also used to prove the existence of certain IPP codes.We prove a precise formula for F(3,q), construct maximum IPP codes with size F(3,q), and give an efficient decoding algorithm for such codes. The main techniques used in this thesis are from graph theory and nonlinear optimization. Our approach may be used to improve bounds on F(2k+1, q). Forexample, we characterize the associated graphs ofmaximum IPP codes of length 5, and obtain bounds on F(5,q).