#TITLE_ALTERNATIVE#
Self-dual MDS and MDR codes have speciality in detecting and correcting errors. MDS and MDR codes have the greatest minimum distance compare with the other codes with the same length and dimension. Beside this, there are near-MDS...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/17630 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Self-dual MDS and MDR codes have speciality in detecting and correcting errors. MDS and MDR codes have the greatest minimum distance compare with the other codes with the same length and dimension. Beside this, there are near-MDS <br />
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and near-MDR codes that have the smallest difference of minimum distance with MDS or MDR codes. This means that the capability of near-MDS and near-MDR codes in detecting and correcting errors are almost the same with MDS or MDR <br />
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codes. Nowadays, interest in codes over rings and linear codes over finite rings have been increased. In this thesis I constructed new self-dual MDS or MDR or near MDS or near-MDR codes over Zpq. There are 19 new near-MDR codes over Z65 with length 10 and 33 new codes over Z65 with length 8 that consist of 10 MDR codes, 1 near-MDR code, and 22 near-MDS codes. I also constructed 29 codes over Z85 with <br />
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length 8 that consist of 9 MDR codes, 2 near-MDR codes and 18 near-MDS. Beside them, there are 5 new self-dual codes over Z221 with length 4 that consist of 1 MDS code and 4 near-MDS codes. For codes over Z221 with length 6, I constructed 16 new self-dual codes that consist of 1 MDS code, 3 MDR codes, 4 near-MDS codes, and 8 near-MDR codes. I also constructed 30 new self-dual codes over Z221 with <br />
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length 8 that consist of 6 MDR codes, 20 near-MDS codes, and 4 near-MDR codes. |
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