Two classes of two-weight linear codes over finite fields

Abstract

Let $ p\equiv 1\pmod 4 $ be a prime, $ m $ a positive integer, $ \frac{\phi(p^m)}2 $ the multiplicative order of $ 2 $ modulo $ p^m $, and let $ q = 2^{ \frac{\phi(p^m)}2} $, where $ \phi(\cdot) $ 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.

Keywords

• exponential sum
• cyclotomy
• linear code
• two-weight code