Applications of n-to-1 Mappings in Difference Families and Optimal Constant Weight Codes
来源：
发布时间：2026-11-03
报告时间：- 2026年11月5日 （周四）上午8:00-10:00
- 报告地点：
- 腾讯会议:907889184
- 报告人：
- 衡子灵
- 报告人单位：
- 长安大学
- 邀请人：
- 刘宏伟
- 摘要：
- As a generalization of permutation polynomials, n-to-1 mappings have found applications in finite geometry, cryptography and linear codes. In this talk, we investigate novel applications of n-to-1 mappings over finite fields to the construction of difference families, constant weight codes, and constant composition codes. First, we propose two general constructions for difference families: one based on the preimage sets and the other on the image sets of n-to-1 mappings. For the construction using image sets, we establish necessary and sufficient conditions that guarantee the resulting collection forms a difference family over either the additive or multiplicative group of the finite field. By selecting suitable n-to-1 mappings, we obtain several infinite families of difference families with new parameters, and simultaneously recover a number of previously known families. Second, we give two systematic constructions of constant weight codes and constant composition codes from n-to-1 mappings. We establish some sufficient conditions for these constructions to yield constant weight codes or constant composition codes. Using concrete n-to-1 mappings, we obtain several infinite families of optimal constant weight codes and several infinite families of optimal constant composition codes.
衡子灵(长安大学)
