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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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/64947 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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