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

03/20/2023

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by   Shudi Yang, et al.

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Linear codes are the most important family of codes in coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes, association schemes and strongly regular graphs. By setting p≡ 1 4, we construct an infinite family of linear codes using two weakly regular unbalanced (and balanced) plateaued functions with index p-1/2. Most of our constructed codes have a few weights and are minimal. After analysing their punctured version, we find that they are projective codes containing some optimal ones.