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doctoral thesis
Konstrukcija ekstremalnih Z4-kodova tipa II
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:036156
Ban, Sara
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Ban, S. (2019). Konstrukcija ekstremalnih Z4-kodova tipa II (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:036156

Ban, Sara. "Konstrukcija ekstremalnih Z4-kodova tipa II." Doctoral thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:036156

Ban, Sara. "Konstrukcija ekstremalnih Z4-kodova tipa II." Doctoral thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:036156

Ban, S. (2019). 'Konstrukcija ekstremalnih Z4-kodova tipa II', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 22 March 2025, https://urn.nsk.hr/urn:nbn:hr:217:036156

Ban S. Konstrukcija ekstremalnih Z4-kodova tipa II [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2025 March 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:036156

S. Ban, "Konstrukcija ekstremalnih Z4-kodova tipa II", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:036156

Metadata
TitleKonstrukcija ekstremalnih Z4-kodova tipa II
Title (english)Construction of extremal type II Z4-codes
Title (croatian)Konstrukcija ekstremalnih Z4-kodova tipa II
AuthorSara Ban
MentorSanja Rukavina (mentor)
Committee memberDean Crnković (predsjednik povjerenstva)
Committee memberSanja Rukavina (član povjerenstva)
Committee memberVedran Krčadinac (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-07-08, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
Predmet istraživanja ove doktorske disertacije je konstrukcija ekstremalnih Z4-kodova tipa II, odnosno samodulanih Z4-kodova kod kojih su euklidske težine svih riječi djeljive sa 8 i koji imaju najveću moguću minimalnu euklidsku težinu. Ekstremalne Z4-kodove tipa II konstruiramo iz postojećih ekstremalnih Z4-kodova tipa II i iz binarnih kodova s određenim svojstvima. Cilj je konstrukcija novih ekstremalnih Z4-kodova tipa II.... More Pri konstrukcijama, osim teorijskih rezultata, koristimo programe napisane za uporabu u programskim paketima GAP ([40]) i Magma ([6]). Polazeći od poznate metode konstrukcije ekstremalnih Z4-kodova tipa II za duljine 24; 32 i 40; koja je prikazana u [8], razvijamo metodu konstrukcije ekstremalnih Z4-kodova tipa II za duljine 48; 56 i 64: Primjenom razvijene metode te otprije poznatih metoda iz [35] i [8], pokušavamo konstruirati nove ekstremalne Z4-kodove tipa II. Također, ispitujemo svojstva binarnih kodova pridruženih Hadamardovim matricama te njihovu podobnost za korištenje u konstrukciji ekstremalnih Z4-kodova tipa II. Na ekstremalne Z4-kodove tipa II dobivene polazeći od Hadamardovih matrica primjenjujemo poznate metode iz [8] te u disertaciji razvijene metode s ciljem dobivanja novih ekstremalnih Z4-kodova tipa II. Konstruirani su novi ekstremalni Z4-kodovi tipa II duljina 32 i 40. Iz dobivenih novih ekstremalnih Z4-kodova tipa II duljine 32 konstruiramo kombinatoričke dizajne i grafove koristeći nosače riječi određenih težina te ispitujemo svojstva dobivenih kombinatoričkih struktura. Less
Abstract (english)
The main subject of this dissertation is the construction of extremal Type II Z4-codes. The aim is to construct new extremal Type II Z4-codes. We constructed extremal Type II Z4-codes using known methods and methods developed in this dissertation starting from existing extremal Type II Z4-codes. We also constructed Type II Z4-codes from certain binary codes and examined the extremality of obtained codes. We have been using... More GAP and Magma software packages. Some necessary concepts from coding theory, design theory, graph theory and basic facts about lattices are introduced in the first chapter. Second chapter of the dissertation contains the classification of extremal Type II Z4-codes of lengths 8, 16 and 24 and information about numbers of known extremal Type II Z4-codes of larger lengths. It also contains constructions of self-dual Z4-codes and Type II Z4-codes from binary codes with certain properties. We have been trying to construct new extremal Type II Z4-codes of lengths 56 and 64 starting from some binary codes. Third chapter of the dissertation contains three constructions of extremal Type II Z4-codes from existing extremal Type II Z4-codes. We corrected errors in the first construction and obtained new extremal Type II Z4-codes of length 32 in that way. Starting from known methods for construction of extremal Type II Z4-codes of lengths 24; 32 and 40 we developed a method for construction of extremal Type II Z4-codes of lengths 48; 56 and 64. We have been trying to construct new extremal Type II Z4-codes using this method. The second construction was used to get new extremal Type II Z4-codes of length 40. We tried to construct new extremal Type II Z4-codes of lengths 56 and 64 starting from certain existing extremal Type II Z4-codes of lengths 56 and 64 using the first and the third construction in this chapter. We showed that new extremal Type II Z4-codes of lengths 56 and 64 cannot be obtained in this way. In the next part of the dissertation we looked at the binary codes associated with Hadamard matrices. Their properties were analyzed. We proved their suitability for construction of extremal Type II Z4-codes introduced in the second chapter of the dissertation. New extremal Type II Z4-codes of lengths 32 and 40 were obtained with the use of Hadamard matrices. The last, fifth chapter, is devoted to constructing combinatorial designs and graphs using supports of codewords with specific weights of the obtained new extremal Type II Z4-codes of length 32. Properties of the constructed structures were analyzed. We tried to construct new designs and distance-regular or strongly-regular graphs. Parameters of all obtained designs are known. We obtained some regular graphs which are not distance-regular. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:036156
Study programmeTitle: Mathematics
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
Type of resourceText
Extentiv, 103 str.
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-07-17 12:48:36
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