Self-dual codes, subcode structures, and applications.

Error-correcting codes;Coding theory;Self-dual codes;Optimum distance profile;Complementary information set;Network coding theory

Finley James Freibert

University:University of Louisville

Department:Mathematics

关键词: Error-correcting codes;    Coding theory;    Self-dual codes;    Optimum distance profile;    Complementary information set;    Network coding theory;   

Others  :  https://ir.library.louisville.edu/cgi/viewcontent.cgi?article=1456&context=etd

美国|英语

来源: The Universite of Louisville's Institutional Repository

【 摘 要 】

The classification of self-dual codes has been an extremely active area incoding theory since 1972 [33]. A particularly interesting class of self-dual codesis those of Type II which have high minimum distance (called extremal or near-extremal).It is notable that this class of codes contains famous unique codes:the extended Hamming [8,4,4] code, the extended Golay [24,12,8] code, and theextended quadratic residue [48,24,12] code. We examine the subcode structuresof Type II codes for lengths up to 24, extremal Type II codes of length 32, and givepartial results on the extended quadratic residue [48,24,12] code. We also developa generalization of self-dual codes to Network Coding Theory and give some resultson existence of self-dual network codes with largest minimum distance for lengthsup to 10. Complementary Information Set (CIS for short) codes, a class of classicalcodes recently developed in [7], have important applications to Cryptography. CIScodes contain self-dual codes as a subclass. We give a new classification result forCIS codes of length 14 and a partial result for length 16.