Construction of Self-dual (near) MDS or (near) MDR Codes over Finite Ring Zpm
A linear code C of length n with minimum distance d over Zm is a submodule of (Zm)n, where Zm is a nite ring of integer modulo m. If d = n????rank (C)+1, then C is called a Maximum Distance with respect to Rank (MDR) code and if the rank is equal to the free rank then C is called a Maximum Distan...
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| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/37312 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A linear code C of length n with minimum distance d over Zm is a submodule
of (Zm)n, where Zm is a nite ring of integer modulo m. If d = n????rank (C)+1, then
C is called a Maximum Distance with respect to Rank (MDR) code and if the rank
is equal to the free rank then C is called a Maximum Distance Separable (MDS)
code. In this thesis, we present a method for constructing self-dual codes over nite
rings Zpm with p an odd prime and m a positive integer by Lee and Lee (2008).
We use their generator matrices as inputs. Using this method, we obtain new self-
orthogonal or self-dual MDS, MDR, near MDS, or near MDR codes of length at
least up to 10 over various nite rings Zpm with pm = 25; 125; 169; 289. |
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