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Two Families of Optimal Linear Codes and Their Subfield Codes
- Source :
- IEEE Transactions on Information Theory. 66:6872-6883
- Publication Year :
- 2020
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2020.
-
Abstract
- 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.
- Subjects :
- 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
Subjects
Details
- ISSN :
- 15579654 and 00189448
- Volume :
- 66
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Information Theory
- Accession number :
- edsair.doi...........5e26d024d91c08262c27ee21b89767b0