A link between combinatorial designs and three-weight linear codes

作者：Olmez Oktay^*

来源：Designs, Codes and Cryptography, 2018, 86(4): 817-833.

DOI：10.1007/s10623-017-0363-3

• Partial geometric designs
• Partial geometric difference sets
• Weakly regular bent functions
• Almost bent functions
• Plateaued functions
• Three-weight linear codes
• Strongly regular graphs

In this paper, we show that partial geometric designs can be constructed from certain three-weight linear codes, almost bent functions and ternary weakly regular bent functions. In particular, we show that existence of a family of partial geometric difference sets is equivalent to existence of a certain family of three-weight linear codes. We also provide a link between ternary weakly regular bent functions, three-weight linear codes and partial geometric difference sets.

• 出版日期2018-4