Speaker: 朱力，贵州师范大学

Title: The multiple equal-difference structure of cyclotomic cosets

Language: Chinese

Time & Venue: 2026.09.16 14:00-16:00 南楼N226

Abstract: Cyclotomic coset is a classical notion in the theory of finite field, which has wide applications in problems from coding theory and cryptography. In this talk we will introduce the definition of equal-difference cyclotomic coset, which are cosets endowed with a structure of a coset with respect to a subgroup of $\mathbb{Z}/n\mathbb{Z}$. For the general case, we prove that any cyclotomic coset has a multiple equal-difference structure, that is, it can be decomposed into a disjoint union of equal-difference subsets. We construct an anti-order-preserving one-to-one correspondence, between the multiple equal-difference representations of the q-cyclotomic cosets modulo n and the irreducible factorizations of $X^{n}-1$ into binomials over extension fields of $\mathbb{F}_{q}$. As an application, we present an algorithm to simplify the computation of the leaders of cyclotomic cosets. This is a joint work with Zhou Juncheng, Liu Jinle and Wu Hongfeng.