Linear Codes Constructed from Two Weakly Regular Plateaued Functions with Index (<i>p</i> − 1)/2

Abstract

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.

Keywords

• linear code
• weight distribution
• Walsh transform
• plateaued function