LINEAR CODES OVER Z4: STRUCTURES, CONSTRUCTIONS, AND GENERALIZATIONS
In this thesis, we explore the structure and construction methods of linear codes over Z4 as well as their generalizations. We study the structure of skew-cyclic codes with derivation over R := Z4 + vZ4, v2 = v and their use in the construction of linear codes over Z4. We also present some method...
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id-itb.:649472022-06-17T09:13:01ZLINEAR CODES OVER Z4: STRUCTURES, CONSTRUCTIONS, AND GENERALIZATIONS Christofen Tang, Hopein Indonesia Theses Z4-linear code, skew-cyclic code with derivation, optimal code, two- Lee-weight code. INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/64947 In this thesis, we explore the structure and construction methods of linear codes over Z4 as well as their generalizations. We study the structure of skew-cyclic codes with derivation over R := Z4 + vZ4, v2 = v and their use in the construction of linear codes over Z4. We also present some methods to construct new linear codes over Z4 from the known ones. Some of these new codes are optimal. We obtained all optimal linear codes for k1 = 2, k2 = 0 and many optimal linear codes for k1 = 3, k2 = 0. Moreover, we obtained a family of optimal two-Lee-weight codes. text |
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Institut Teknologi Bandung |
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Asia |
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Indonesia Indonesia |
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Indonesia |
| description |
In this thesis, we explore the structure and construction methods of linear codes
over Z4 as well as their generalizations. We study the structure of skew-cyclic
codes with derivation over R := Z4 + vZ4, v2 = v and their use in the construction
of linear codes over Z4. We also present some methods to construct new linear
codes over Z4 from the known ones. Some of these new codes are optimal. We
obtained all optimal linear codes for k1 = 2, k2 = 0 and many optimal linear codes
for k1 = 3, k2 = 0. Moreover, we obtained a family of optimal two-Lee-weight
codes. |
| format |
Theses |
| author |
Christofen Tang, Hopein |
| spellingShingle |
Christofen Tang, Hopein LINEAR CODES OVER Z4: STRUCTURES, CONSTRUCTIONS, AND GENERALIZATIONS |
| author_facet |
Christofen Tang, Hopein |
| author_sort |
Christofen Tang, Hopein |
| title |
LINEAR CODES OVER Z4: STRUCTURES, CONSTRUCTIONS, AND GENERALIZATIONS |
| title_short |
LINEAR CODES OVER Z4: STRUCTURES, CONSTRUCTIONS, AND GENERALIZATIONS |
| title_full |
LINEAR CODES OVER Z4: STRUCTURES, CONSTRUCTIONS, AND GENERALIZATIONS |
| title_fullStr |
LINEAR CODES OVER Z4: STRUCTURES, CONSTRUCTIONS, AND GENERALIZATIONS |
| title_full_unstemmed |
LINEAR CODES OVER Z4: STRUCTURES, CONSTRUCTIONS, AND GENERALIZATIONS |
| title_sort |
linear codes over z4: structures, constructions, and generalizations |
| url |
https://digilib.itb.ac.id/gdl/view/64947 |
| _version_ |
1822932588929482752 |