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 only have a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs. By setting p≡1(mod4), we constructed an infinite family of linear codes using two distinct weakly regular unbalanced (and balanced) plateaued functions with index (p-1)/2. Their weight distributions were 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.

Optimal decay rates for the compressible viscoelastic flows.

In this paper, we study the compressible viscoelastic flows in three-dimensional whole space. Under the assumption of small initial data, we establish the unique global solution by the energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solution if the initial data belong to L1(ℝ3) additionally.