2015/04/06 by Maosheng Xiong, Xiong, Maosheng, Shuxing Li +3 · 3 citations
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #Cryptographic Implementations and Security #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1504.01274
openalex publication_date 2015/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generalized Hamming weights (GHWs) of linear codes are fundamental parameters, the knowledge of which is of great interest in many applications. However, to determine the GHWs of linear codes is difficult in general. In this paper, we study the GHWs for a family of reducible cyclic codes and obtain the complete weight hierarchy in several cases. This is achieved by extending the idea of \citeYLFL into higher dimension and by employing some interesting combinatorial arguments. It shall be noted that these cyclic codes may have arbitrary number of nonzeroes.