Type II codes over Z4 x Z4
Date of Publication
1999
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Subject Categories
Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Yolando B. Beronque
Defense Panel Chair
Jose Maria P. Balmaceda
Defense Panel Member
Severino V. Gervacio
Blessilda P. Raposa
Jumela F. Sarmiento
Arlene A. Pascasio
Abstract/Summary
This study aims to give a characterization of Type II codes over Z4 x Z4 with respect to some selected weight functions and the distinct dualities of the group Z4 x Z4. It includes a construction method in the generation of self-dual codes for any given duality of Z4 x Z4 and in the generation of Type II codes for some weight functions satisfying the squareness property.In this paper, it is shown that the 32 dualities of Z4 x Z4 can be reduced to 4 inequivalent forms. Moreover, the list of T solutions associated with each duality is reducible by eliminating those solutions that can be obtained by inter-changing the weight assignments of the alphabets and those solutions that can be derived by changing the n values in the diagonal representation of T in the form Diag(na0,na1,...na15). The construction method described here relates codes over Z4 x Z4 and two binary codes C1 and C2 with the property that C1 (-C2. The author used the Mathematica programming language in writing some computer routines to verify the theorems which were formulated and generate some examples of certain codes.This research is not exhaustive as far as describing all Type II codes over Z4 x Z4 with respect to all possible combinations of dualities and T solutions is concerned. The author intentionally chose only four cases of these combinations which she would describe as interesting because of (1) some properties that these codes possess and (2) a construction method that can be applied to all of them.
Abstract Format
html
Language
English
Format
Accession Number
TG02986
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
108 numb. leaves ; Computer print-out
Keywords
Group theory; Abelian groups; Representations of groups
Recommended Citation
Nocon, E. G. (1999). Type II codes over Z4 x Z4. Retrieved from https://animorepository.dlsu.edu.ph/etd_doctoral/836