Minimal Binary Linear Codes
Cunsheng Ding, Ziling Heng, Zhengchun Zhou · IEEE Transactions on Information Theory · 2018
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 Wmin/Wmax≤ 1/2 from a generic construction, where Wminand Wmax, respectively, denote the minimum and maximum nonzero weights in a code. The weight distributions of all these minimal binary linear codes are also determined.