Novel Indexing of Cyclic Codes with Run-Length Applications
© 2013 IEEE. Any cyclic code over a finite field can be considered as a sum of some non-degenerate irreducible cyclic codes. We use the traditional trace function representation of irreducible cyclic codes to suggest a similar representation to any cyclic code. This representation suggests an indexi...
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| Main Authors: | , , |
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| Format: | Journal |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85077237154&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67762 |
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| Institution: | Chiang Mai University |
| Summary: | © 2013 IEEE. Any cyclic code over a finite field can be considered as a sum of some non-degenerate irreducible cyclic codes. We use the traditional trace function representation of irreducible cyclic codes to suggest a similar representation to any cyclic code. This representation suggests an indexing for codewords of the cyclic code. Specifically, each codeword is identified by a triplet IA,RA and QA. The relationship between these triplets was studied for codewords that are cyclic shifts of each other. We introduce a set SC whose elements correspond to subsets that each contains all the cyclic shifts of a codeword. As an application to the proposed indexing, we take advantage of the trace function linearity to explore codewords with a specific run-length. Because the run-length is invariant to cyclic shifts, it suffices to explore elements of SC that match codewords with a specific run-length. Instead of searching at the code for these codewords, the problem is turned into solving a system of linear equations. |
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