Open AccessDUAL CODE AND MACWILLIAMS IDENTITY ON ADDITIVE CODE
Author(s) -
Miftah Yuliati,
Sri Wahyuni,
Indah Emilia Wijayanti
Publication year - 2019
Publication title -
jurnal matematika thales
Language(s) - English
Resource type - Journals
ISSN - 2715-1891
DOI - 10.22146/jmt.34471
Subject(s) - dual code , cyclic code , constant weight code , polynomial code , weight distribution , code (set theory) , hamming code , mathematics , systematic code , universal code , linear code , hamming bound , dual (grammatical number) , product (mathematics) , discrete mathematics , computer science , code rate , algorithm , programming language , decoding methods , physics , block code , art , geometry , literature , set (abstract data type) , thermodynamics
Additive code is a generalization of linear code. It is defined as subgroup of a finite Abelian group. The definitions of Hamming distance, Hamming weight, weight distribution, and homogeneous weight distribution in additive code are similar with the definitions in linear code. Different with linear code where the dual code is defined using inner product, additive code using theories in group to define its dual code because in group theory we do not have term of inner product. So, by this thesis, the definitions of dual code in additive code will be discussed. Then, this thesis discuss about a familiar theorem in dual code theory, that is MacWilliams Identity. Next, this thesis discuss about how to proof of MacWilliams Identity on adiitive code using dual codes which are defined.