LINEARITY OF IMAGES CODE OVER THE FINITE RING
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 pro...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/68296 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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