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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id-itb.:373122019-03-20T15:16:10ZConstruction of Self-dual (near) MDS or (near) MDR Codes over Finite Ring Zpm Azalia, Ulima Ilmu alam dan matematika Indonesia Theses nite ring, self-dual codes, self-orthogonal codes, MDS codes, near MDS codes, MDR codes, near MDR codes. INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/37312 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. text |
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Institut Teknologi Bandung |
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Indonesia Indonesia |
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Indonesia |
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Ilmu alam dan matematika |
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Ilmu alam dan matematika Azalia, Ulima Construction of Self-dual (near) MDS or (near) MDR Codes over Finite Ring Zpm |
| description |
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. |
| format |
Theses |
| author |
Azalia, Ulima |
| author_facet |
Azalia, Ulima |
| author_sort |
Azalia, Ulima |
| title |
Construction of Self-dual (near) MDS or (near) MDR Codes over Finite Ring Zpm |
| title_short |
Construction of Self-dual (near) MDS or (near) MDR Codes over Finite Ring Zpm |
| title_full |
Construction of Self-dual (near) MDS or (near) MDR Codes over Finite Ring Zpm |
| title_fullStr |
Construction of Self-dual (near) MDS or (near) MDR Codes over Finite Ring Zpm |
| title_full_unstemmed |
Construction of Self-dual (near) MDS or (near) MDR Codes over Finite Ring Zpm |
| title_sort |
construction of self-dual (near) mds or (near) mdr codes over finite ring zpm |
| url |
https://digilib.itb.ac.id/gdl/view/37312 |
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1823638115292545024 |