Linear Codes Constructed From Two Weakly Regular Plateaued Functions with Index (p-1)/2

Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs. By setting $p\equiv 1 \pmod 4$, we construct an infinite family of linear codes using two distinct weakly regular unbalanced (and balanced) plateaued functions with index $(p-1)/2$. Their weight distributions are completely determined by applying exponential sums and Walsh transform. As a result, most of our constructed codes have a few nonzero weights and are minimal.