2015/11/06 by Can Xiang, Keqin Feng, Xiang, Can +3 · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1511.02264
openalex publication_date 2015/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a construction of linear codes over \f2t from Boolean functions, which is a generalization of Ding's method \cite[Theorem 9]Ding15. Based on this construction, we give two classes of linear codes \Cf and \Cf (see Theorem \refthm-maincode1 and Theorem \refthm-maincodenew) over \f2t from a Boolean function f:\fq→ \f2, where q=2n and \f2t is some subfield of \fq. The complete weight enumerator of \Cf can be easily determined from the Walsh spectrum of f, while the weight distribution of the code \Cf can also be easily settled. Particularly, the number of nonzero weights of \Cf and \Cf is the same as the number of distinct Walsh values of f. As applications of this construction, we show several series of linear codes over \f2t with two or three weights by using bent, semibent, monomial and quadratic Boolean function f.