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Bibliographic Data
Control Number311043
Date and Time of Latest Transaction20150706092100.AM
General Information150706s |||||||||b ||00|||
Cataloging SourceSTII-DOST
Local Call Number(T) QA268 N38 2004
Main Entry - Personal NameNatividad, Ann Marie A.
Title StatementFrom cyclic to quasi-cyclic codes by Ann Marie A. Natividad
Physical Description[vi], 124 leaves figures
Summary, Etc.We begin by considering binary l-quasi-cyclic codes of lengths a multiple of 3,5 and 7. These codes are respectively called cubic, quantic and septic codes. By the construction of these types of codes given in [30], it becomes evident that l-quasi-cyclic codes result from combining smaller constituent codes of length l. In this dissertation, we will assume the case when the constituent codes of a quasi-cyclic code C are cyclic. By using the results in [30] together with the Mattson-Solomon polynomial associated with a codewords and the inversion formula, we obtain the trace representation of codewords in C and show that C is cylcic. This enables us to express the nonzeros of C as a function of the nonzeros of the smaller constituent codes. We then summarize these results by giving the check polynomial of C in terms of the check polynomial of the constituent codes. Then, using what we know of codes over finite chain rings and the construction of quasi-cyclic codes given in [31], we are able to extend out results for the binary case to codes over Z4, also known as quaternary codes are cyclic, then the resulting quaternary code is also cyclic. Moreover, we can express the chec polynomial of the bigger code in terms of the check polynomials of its constituent codes. The second half of this dissertation is made up of applications of the theoretical results obtained. We use quadratic residue codes, the trace orthogonal basis and other known quaternary self-dual codes to construct cubic quaternary self-dual codes with good minimum Euclidean and Lee weight. We are also able to construct a new quaternary self-dual code of length 38. And finally, we use the random construction of codes over GR(4,) and quintic construction to come up with quaternary self-dual codes with good minimum Euclidean and Lee weight
Subject Added Entry - Topical TermMathematics
 Coding theory
 Dual-coding hypothesis
LocationDOST STII (T) QA268 N38 2004 THESES T STI-13-2238 1 14-15378 Donation 2013-05-20
  
     
 
Physical Location
Department of Science and Technology
Science and Technology Information Institute(T) QA268 N38 2004
  
     
 
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