Two classes of two-weight linear codes over finite fields.

Let p ≡ 1 (mod 4) be a prime, m a positive integer, ϕ (p m) 2 the multiplicative order of 2 modulo p m , and let q = 2 ϕ (p m) 2 , where ϕ (⋅) is the Euler's function. In this paper, we construct two classes of linear codes over F q and investigate their weight distributions. By calculating two classes of special exponential sums, the desired results are obtained. Let be a prime, a positive integer, the multiplicative order of modulo , and let , where is the Euler's function. In this paper, we construct two classes of linear codes over and investigate their weight distributions. By calculating two classes of special exponential sums, the desired results are obtained. [ABSTRACT FROM AUTHOR]