New non-primitive codes formed from primitive BCH and Hamming codes and their norm evaluation
Integrated studies completion of BCH codes of different lengths is devoted. Most attention is paid to codes whose lengths are intermediate between primitive lengths, which are obtained by throwing in a special way from the check matrices of primitive BCH codes of a large number of columns, but with...
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| Format: | Article |
| Language: | Russian |
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Educational institution «Belarusian State University of Informatics and Radioelectronics»
2019-06-01
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| Series: | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
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| Online Access: | https://doklady.bsuir.by/jour/article/view/1102 |
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| _version_ | 1849243476576698368 |
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| author | V. K. Konopelko V. A. Lipnitski |
| author_facet | V. K. Konopelko V. A. Lipnitski |
| author_sort | V. K. Konopelko |
| collection | DOAJ |
| description | Integrated studies completion of BCH codes of different lengths is devoted. Most attention is paid to codes whose lengths are intermediate between primitive lengths, which are obtained by throwing in a special way from the check matrices of primitive BCH codes of a large number of columns, but with preservation of cyclical properties, which are proposed to be called non-primitive BCH codes. The properties of the named code class are systematically investigated. It is proved that, according to the variety of lengths, about a third of the non-primitive BCH codes have a code distance greater than constructive, and, therefore, they are able to correct random errors, the multiplicity of which significantly exceeds the constructive frame. Correction of such errors is called plus-decoding. It is shown that it is impossible to implement plus-decoding by known classical methods and algorithms, but only by the available and developing means of the theory of norms syndromes. Two algorithms for the implementation of plus-decoding by permutation normal methods are proposed. Non-primitive BCH-codes are promising for applications in real modern information and communication systems. |
| format | Article |
| id | doaj-art-9d1b60bfb6fa4840848adb8642d802c1 |
| institution | Kabale University |
| issn | 1729-7648 |
| language | Russian |
| publishDate | 2019-06-01 |
| publisher | Educational institution «Belarusian State University of Informatics and Radioelectronics» |
| record_format | Article |
| series | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
| spelling | doaj-art-9d1b60bfb6fa4840848adb8642d802c12025-08-20T03:59:27ZrusEducational institution «Belarusian State University of Informatics and Radioelectronics»Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki1729-76482019-06-010312241101New non-primitive codes formed from primitive BCH and Hamming codes and their norm evaluationV. K. Konopelko0V. A. Lipnitski1Belarusian state university of informatics and radioelectronicsMilitary academy of Republic of BelarusIntegrated studies completion of BCH codes of different lengths is devoted. Most attention is paid to codes whose lengths are intermediate between primitive lengths, which are obtained by throwing in a special way from the check matrices of primitive BCH codes of a large number of columns, but with preservation of cyclical properties, which are proposed to be called non-primitive BCH codes. The properties of the named code class are systematically investigated. It is proved that, according to the variety of lengths, about a third of the non-primitive BCH codes have a code distance greater than constructive, and, therefore, they are able to correct random errors, the multiplicity of which significantly exceeds the constructive frame. Correction of such errors is called plus-decoding. It is shown that it is impossible to implement plus-decoding by known classical methods and algorithms, but only by the available and developing means of the theory of norms syndromes. Two algorithms for the implementation of plus-decoding by permutation normal methods are proposed. Non-primitive BCH-codes are promising for applications in real modern information and communication systems.https://doklady.bsuir.by/jour/article/view/1102minimum code distanceerror multiplicitybch codeerror syndromecode automorphism |
| spellingShingle | V. K. Konopelko V. A. Lipnitski New non-primitive codes formed from primitive BCH and Hamming codes and their norm evaluation Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki minimum code distance error multiplicity bch code error syndrome code automorphism |
| title | New non-primitive codes formed from primitive BCH and Hamming codes and their norm evaluation |
| title_full | New non-primitive codes formed from primitive BCH and Hamming codes and their norm evaluation |
| title_fullStr | New non-primitive codes formed from primitive BCH and Hamming codes and their norm evaluation |
| title_full_unstemmed | New non-primitive codes formed from primitive BCH and Hamming codes and their norm evaluation |
| title_short | New non-primitive codes formed from primitive BCH and Hamming codes and their norm evaluation |
| title_sort | new non primitive codes formed from primitive bch and hamming codes and their norm evaluation |
| topic | minimum code distance error multiplicity bch code error syndrome code automorphism |
| url | https://doklady.bsuir.by/jour/article/view/1102 |
| work_keys_str_mv | AT vkkonopelko newnonprimitivecodesformedfromprimitivebchandhammingcodesandtheirnormevaluation AT valipnitski newnonprimitivecodesformedfromprimitivebchandhammingcodesandtheirnormevaluation |