The Dimension of Subcode-Subfields of Shortened Generalized Reed Solomon Codes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2011
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| _version_ | 1866916228353753088 |
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| author | Hernando, Fernando Marshall, Kyle O'Sullivan, Michael E. |
| author_facet | Hernando, Fernando Marshall, Kyle O'Sullivan, Michael E. |
| contents | Reed-Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where the length is static, the appropriate length can be obtained by an RS code by shortening or puncturing. Generalized Reed-Solomon (GRS) codes are a generalization of RS codes, whose subfield-subcodes are extensively studied. In this paper we show that a particular class of GRS codes produces many subfield-subcodes with large dimension. An algorithm for searching through the codes is presented as well as a list of new codes obtained from this method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1108_5475 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | The Dimension of Subcode-Subfields of Shortened Generalized Reed Solomon Codes Hernando, Fernando Marshall, Kyle O'Sullivan, Michael E. Information Theory 14G50, 11T71, 94B65 Reed-Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where the length is static, the appropriate length can be obtained by an RS code by shortening or puncturing. Generalized Reed-Solomon (GRS) codes are a generalization of RS codes, whose subfield-subcodes are extensively studied. In this paper we show that a particular class of GRS codes produces many subfield-subcodes with large dimension. An algorithm for searching through the codes is presented as well as a list of new codes obtained from this method. |
| title | The Dimension of Subcode-Subfields of Shortened Generalized Reed Solomon Codes |
| topic | Information Theory 14G50, 11T71, 94B65 |
| url | https://arxiv.org/abs/1108.5475 |