Reed-Solomon codes are a well known family of error-correcting codes with many good properties. However, they require a finite field to operate, limiting the alphabet size to a prime power. In this work, we build a weaker algebraic structure which supports alphabet of any integer size and requires only standard addition, multiplication and division to implement. Then we study a family of error-correcting codes based on matrix multiplication over this structure. We also adapt the Reed-Solomon code principle on this code family and study its properties. We prove and verify experimentally that while a random code of this family has high distance, the Reed-Solomon adaptation fails to perform well. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:456111 |
| Date | January 2022 |
| Creators | Končický, Václav |
| Contributors | Koucký, Michal, Mareš, Martin |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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