Two Families of Optimal Linear Codes and Their Subfield Codes
| العنوان: | Two Families of Optimal Linear Codes and Their Subfield Codes |
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| المؤلفون: | Cunsheng Ding, Qiuyan Wang, Ziling Heng |
| المصدر: | IEEE Transactions on Information Theory. 66:6872-6883 |
| بيانات النشر: | Institute of Electrical and Electronics Engineers (IEEE), 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Combinatorics, 0202 electrical engineering, electronic engineering, information engineering, 020206 networking & telecommunications, Dual polyhedron, 02 engineering and technology, Library and Information Sciences, Prime power, BCH code, Griesmer bound, Computer Science Applications, Information Systems |
| الوصف: | In this paper, a family of $[{q}^{2}-1, 4, {q}^{2}-{q}-2]$ cyclic codes over ${\mathbb F}_{{q}}$ meeting the Griesmer bound is presented. Their duals are $[{q}^{2}-1,{q}^{2}-5,4]$ almost MDS codes and are optimal with respect to the sphere-packing bound. The ${q}_{0}$ -ary subfield codes of this family of cyclic codes are also investigated, where ${q}_{0}$ is any prime power such that q is power of ${q}_{0}$ . Some of the subfield codes are optimal and some have the best known parameters. It is shown that the subfield codes are equivalent to a family of primitive BCH codes and thus the parameters of the BCH codes are solved. The duals of the subfield codes are also optimal with respect to the sphere-packing bound. A family of $[{q}^{2}, 4, {q}^{2}-{q}-1]$ linear codes over ${\mathbb F}_{{q}}$ meeting the Griesmer bound is presented. Their duals are $[{q}^{2},{q}^{2}-4,4]$ almost MDS codes and are optimal with respect to the sphere-packing bound. The ${q}_{0}$ -ary subfield codes of this family of linear codes are also investigated, where ${q}_{0}$ is any prime power such that q is power of ${q}_{0}$ . Five infinite families of 2-designs are also constructed with three families of linear codes of this paper. |
| تدمد: | 1557-9654 0018-9448 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::5e26d024d91c08262c27ee21b89767b0 https://doi.org/10.1109/tit.2020.3006846 |
| حقوق: | CLOSED |
| رقم الأكسشن: | edsair.doi...........5e26d024d91c08262c27ee21b89767b0 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15579654 00189448 |
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