Minimal binary linear codes
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≤ 1/2 from a
generic construction, where W min and W max, respectively, denote the minimum and …
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≤ 1/2 from a
generic construction, where W min and W max, respectively, denote the minimum and …
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 ≤ 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.
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