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A Subfield-Based Construction of Optimal Linear Codes Over Finite Fields.
- Source :
- IEEE Transactions on Information Theory; Jul2022, Vol. 68 Issue 7, p4408-4421, 14p
- Publication Year :
- 2022
-
Abstract
- In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including infinite families of (near) Griesmer codes. We also characterize the optimality of these four families of linear codes with an explicit computable criterion using the Griesmer bound and obtain many distance-optimal linear codes. In addition, by a more in-depth discussion on some special cases of these four families of linear codes, we obtain several classes of (distance-)optimal linear codes with few weights and completely determine their weight distributions. It is shown that most of our linear codes are self-orthogonal or minimal which are useful in applications. [ABSTRACT FROM AUTHOR]
- Subjects :
- RESEARCH & development
LINEAR codes
FINITE fields
QUANTUM computing
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 157551909
- Full Text :
- https://doi.org/10.1109/TIT.2022.3163651