2016/12/03 by Minjia Shi, Rongsheng Wu, Shi, Minjia +7
Computer Science · Engineering · #94B25 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1612.00915
openalex publication_date 2016/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring R=\mathbbFp+u\mathbbFp+⋯ +uk-1\mathbbFp, with uk=0, are constructed, which generalises \citeSL, the special case of p=k=2. These codes are defined as trace codes. In some cases of their defining sets, they are abelian. Their homogeneous weight distributions are computed by using exponential sums. In particular, in the two-weight case, we give some conditions of optimality of their Gray images by using the Griesmer bound. Their dual homogeneous distance is also given. The codewords of these codes are shown to be minimal for inclusion of supports, a fact favorable to an application to secret sharing schemes.