Three classes of linear codes with two or three weights

In this paper, we mainly determine the weight distributions of three classes of linear codes. Firstly, we prove that two classes of ternary linear codes from the following two planar functions have two or three weights: f ( x ) = x 3 k + 1 2 , x ź F 3 m , where k , m are odd, gcd ( m , k ) = 1 , and f ( x ) = x 3 k + 1 , x ź F 3 m , where m gcd ( m , k ) is odd. They are exactly a part of the open problem in Ding and Ding (2015 Section IV). Secondly, we construct a new class of binary linear codes with three weights. In particular, the linear codes in this paper have applications in consumer electronics, communication and secret sharing schemes.

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