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Minimal Binary Linear Codes.
- Source :
-
IEEE Transactions on Information Theory . Oct2018, Vol. 64 Issue 10, p6536-6545. 10p. - Publication Year :
- 2018
-
Abstract
- In addition to their applications in data communication and storage, linear codes also have nice applications in combinatorics and cryptography. Minimal linear codes, a special type of linear codes, are preferred in secret sharing. In this paper, a necessary and sufficient condition for a binary linear code to be minimal is derived. This condition enables us to obtain three infinite families of minimal binary linear codes with $w_{\min }/w_{\max } \leq 1/2$ from a generic construction, where $w_{\min }$ and $w_{\max }$ , respectively, denote the minimum and maximum nonzero weights in a code. The weight distributions of all these minimal binary linear codes are also determined. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 64
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 131794614
- Full Text :
- https://doi.org/10.1109/TIT.2018.2819196