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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.10833 |
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| _version_ | 1866909205616656384 |
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| author | Yang, Shudi Zhang, Tonghui Yao, Zheng-An |
| author_facet | Yang, Shudi Zhang, Tonghui Yao, Zheng-An |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10833 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Linear Codes Constructed From Two Weakly Regular Plateaued Functions with Index (p-1)/2 Yang, Shudi Zhang, Tonghui Yao, Zheng-An Information Theory 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. |
| title | Linear Codes Constructed From Two Weakly Regular Plateaued Functions with Index (p-1)/2 |
| topic | Information Theory |
| url | https://arxiv.org/abs/2303.10833 |