Type II codes over Z4 x Z4

• Main Author: Nocon, Ederlina G.
• Format: text
• Language: English
• Published: Animo Repository 1999
• Subjects: Group theory; Abelian groups; Representations of groups; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_doctoral/836
• Institution: De La Salle University

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.