Two classes of two-weight linear codes over finite fields - Jianying Rong; Fengwei Li; Ting Li (AIMS Mathematics, 2023)
Let $ p\equiv 1\pmod 4 $ be a prime, $ m $ a positive integer, $ \frac{φ(p^m)}2 $ the multiplicative order of $ 2 $ modulo $ p^m $, and let $ q = 2^{ \frac{φ(p^m)}2} $, where $ φ(·) $ is the Euler's function. In this paper, we construct two classes of linear codes over $ \Bbb F_q $ and investigate their weight distributions. By calculating two classes of special exponential sums, the desired results are obtained.