Weight Distribution of a Class of Linear Codes

Xina ZHANG  Xiaoni DU  Rong WANG  Fujun ZHANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E104-A   No.2   pp.399-403
Publication Date: 2021/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2020SDP0003
Type of Manuscript: Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)
Category: Coding Theory
Keyword: 
linear codes,  Gauss sums,  weight distribution,  

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Summary: 
Linear codes with a few weights have many applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs, and they are also of importance in consumer electronics, communications and data storage systems. In this paper, based on the theory of defining sets, we present a class of five-weight linear codes over $mathbb{F}_p$(p is an odd prime), which include an almost optimal code with respect to the Griesmer bound. Then, we use exponential sums to determine the weight distribution.