Obtaining new classes of optimal linear codes by puncturing and shortening optimal cyclic codes
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| Název: | Obtaining new classes of optimal linear codes by puncturing and shortening optimal cyclic codes |
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| Autoři: | Félix Hernández, Gerardo Vega |
| Zdroj: | Applicable Algebra in Engineering, Communication and Computing. 36:1033-1048 |
| Informace o vydavateli: | Springer Science and Business Media LLC, 2024. |
| Rok vydání: | 2024 |
| Témata: | 0102 computer and information sciences, 02 engineering and technology, Puncturing, Computer science, 01 natural sciences, 7. Clean energy, Optical Code Division Multiple Access, Algorithm, Engineering, Cryptanalysis of Block Ciphers and Hash Functions, Artificial Intelligence, Computer Science, Physical Sciences, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Telecommunications, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Mathematics, Cryptography and Error-Correcting Codes |
| Popis: | In this paper we use the puncturing and shortening techniques on two already-known classes of optimal cyclic codes in order to obtain three new classes of optimal linear codes achieving the Griesmer bound. The weight distributions for these codes are settled. We also investigate their dual codes and show that they are either optimal or almost optimal with respect to the sphere-packing bound. Moreover, these duals contain classes of almost maximum distance separable codes which are shown to be proper for error detection. Further, some of the obtained optimal linear codes are suitable for constructing secret sharing schemes with nice access structures. |
| Druh dokumentu: | Article Other literature type |
| Jazyk: | English |
| ISSN: | 1432-0622 0938-1279 |
| DOI: | 10.1007/s00200-024-00653-7 |
| DOI: | 10.60692/yz5b8-47w80 |
| DOI: | 10.60692/2cja7-1fw21 |
| Rights: | CC BY |
| Přístupové číslo: | edsair.doi.dedup.....b0bcf31474ff56b52f8e6426714d2a8c |
| Databáze: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | In this paper we use the puncturing and shortening techniques on two already-known classes of optimal cyclic codes in order to obtain three new classes of optimal linear codes achieving the Griesmer bound. The weight distributions for these codes are settled. We also investigate their dual codes and show that they are either optimal or almost optimal with respect to the sphere-packing bound. Moreover, these duals contain classes of almost maximum distance separable codes which are shown to be proper for error detection. Further, some of the obtained optimal linear codes are suitable for constructing secret sharing schemes with nice access structures. |
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| ISSN: | 14320622 09381279 |
| DOI: | 10.1007/s00200-024-00653-7 |