2022/01/09 by Liu, Haibo, Liao, Qunying
#94A60 #94B05 #94C10 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2201.02981
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then determining their weight distributions have been interesting in coding theory and cryptography. In this paper, a generic construction for binary linear codes with dimension m+2 is presented, then a necessary and sufficient condition for this binary linear code to be minimal is derived. Based on this condition and exponential sums, a new class of minimal binary linear codes violating the Ashikhmin-Barg condition is obtained, and then their weight enumerators are determined.