Two Classes of Linear Codes with Two or Three Weights

Guangkui XU  Xiwang CAO  Jian GAO  Gaojun LUO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2366-2373
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2366
Type of Manuscript: Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)
Category: Coding Theory
Keyword: 
linear code,  Walsh transform,  non-quadratic function,  permutation polynomial,  weight distribution,  

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Summary: 
Many linear codes with two or three weights have recently been constructed due to their applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, two classes of p-ary linear codes with two or three weights are presented. The first class of linear codes with two or three weights is obtained from a certain non-quadratic function. The second class of linear codes with two weights is obtained from the images of a certain function on $mathbb{F}_{p^m}$. In some cases, the resulted linear codes are optimal in the sense that they meet the Griesmer bound.