LINEARITY OF IMAGES CODE OVER THE FINITE RING

• Main Author: Ridwan
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/68296
• Institution: Institut Teknologi Bandung

Linear code is one type of code that is widely studied and continues to be explored by many mathematicians and people who work in coding theory because of its mathematical structure. It also has an efficient encoding and decoding process so that it can correct certain types of errors. In this project, a linear code over a finite ring which can be decomposed from the direct sum of several ideals is studied . Further, the mapping from the finite ring Zn pq to Z2n pq , Zn p2q to Z2n p2q, and Zn pqr to Z3n pqr are defined proven to preserve distance (weight). It’s also proved that the linear code over the finite ring Zpq,Zp2q, and Zpqr with length n and minimum distance d, respectively produce a linear images code with the parameters [2n, k1 + k2 + k3, d], [2n, k1 + k2 + · · · + k5, d], and [3n, k1 + k2 + · · · + k7, d]. In general, linear code over the finite ring Zp1p2···pr produces a linear images code with the parameter [rn, k1+k2+· · ·+k2r?1, d]. In addition, it has also been proven that self-dual code over the finite ring Zpq,Zp2q, and Zpqr returns to images code which is also self-dual code.