On the construction of nonbinary constant-weight codes
Constant-weight codes play an important role in coding theory. Binary constant-weight codes have been extensively investigated. Nonbinary constant-weight codes have also attracted recent attention due to several important applications requiring nonbinary alphabets. However, they are still much les...
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| Format: | Theses and Dissertations |
| Language: | English |
| Published: |
2008
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| Online Access: | http://hdl.handle.net/10356/13622 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | Constant-weight codes play an important role in coding theory. Binary constant-weight
codes have been extensively investigated. Nonbinary constant-weight codes have also
attracted recent attention due to several important applications requiring nonbinary alphabets. However, they are still much less understood than binary constant-weight codes.
In this thesis, we make a thorough study on known constructions of nonbinary constant-
weight codes, and provide new constructions for two in fite families of optimal codes.
The first construction shows that Aq(n, 2w - 1, w) = (q - 1)n/w for all sufficiently large
n satisfying w|(q - 1)n. The second construction uses a novel idea based on sequences to construct optimal q-ary (q, 4, 3)-codes for all q >= 3. |
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