Polynomials generating Hamming codes
A class of polynomials generating q-nary Hamming codes is studied. The criteria for a polynomial to belong to this class are established for the general case and for the case of prime polynomials. The conditions are determined under which reducible polynomials do not belong to the class of polynomia...
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| Date: | 1993 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5881 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512101268717568 |
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| author | Barashko, A. S. Барашко, А. С. Барашко, А. С. |
| author_facet | Barashko, A. S. Барашко, А. С. Барашко, А. С. |
| author_sort | Barashko, A. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:20:04Z |
| description | A class of polynomials generating q-nary Hamming codes is studied. The criteria for a polynomial to belong to this class are established for the general case and for the case of prime polynomials. The conditions are determined under which reducible polynomials do not belong to the class of polynomials generating the q-nary Hamming codes. |
| first_indexed | 2026-03-24T03:23:26Z |
| format | Article |
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| id | umjimathkievua-article-5881 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:23:26Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/06/20eb9405748c688481784fada2318a06.pdf |
| spelling | umjimathkievua-article-58812020-03-19T09:20:04Z Polynomials generating Hamming codes Полиномы, порождающие коды Хэмминга Barashko, A. S. Барашко, А. С. Барашко, А. С. A class of polynomials generating q-nary Hamming codes is studied. The criteria for a polynomial to belong to this class are established for the general case and for the case of prime polynomials. The conditions are determined under which reducible polynomials do not belong to the class of polynomials generating the q-nary Hamming codes. Досліджено клас поліномів, які породжують $q$-кові коди Хемінга (клас ППКХ). Знайдені критерії належності полінома до класу ППКХ у загальному випадку та у випадку, коли поліном є простий. Визначені умови, за яких звідні поліноми не наліжать до класу ППКХ. Institute of Mathematics, NAS of Ukraine 1993-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5881 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 7 (1993); 893–897 Український математичний журнал; Том 45 № 7 (1993); 893–897 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5881/8445 https://umj.imath.kiev.ua/index.php/umj/article/view/5881/8446 Copyright (c) 1993 Barashko A. S. |
| spellingShingle | Barashko, A. S. Барашко, А. С. Барашко, А. С. Polynomials generating Hamming codes |
| title | Polynomials generating Hamming codes |
| title_alt | Полиномы, порождающие коды Хэмминга |
| title_full | Polynomials generating Hamming codes |
| title_fullStr | Polynomials generating Hamming codes |
| title_full_unstemmed | Polynomials generating Hamming codes |
| title_short | Polynomials generating Hamming codes |
| title_sort | polynomials generating hamming codes |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5881 |
| work_keys_str_mv | AT barashkoas polynomialsgeneratinghammingcodes AT baraškoas polynomialsgeneratinghammingcodes AT baraškoas polynomialsgeneratinghammingcodes AT barashkoas polinomyporoždaûŝiekodyhémminga AT baraškoas polinomyporoždaûŝiekodyhémminga AT baraškoas polinomyporoždaûŝiekodyhémminga |