Speaker: 朱力，贵州师范大学

Inviter: 邓映蒲

Title: The arithmetic Singleton bound for simple-root constacyclic codes over finite fields

Language: Chinese

Time & Venue: 2026.09.17 08：30-10：30 南楼N226

Abstract: Constacyclic codes form an important subclass of linear codes which are equipped with a structure of an ideal in a quotient ring of polynomials. There is a common belief that this structure imposes stronger restriction on the Hamming distance of a constacyclic code than the linear structure does, which is supported by many examples. In this talk, we will introduce the notion of a multiple equal-difference representation of the defining set of a squarefree polynomial over a finite field, which describes the symmetry of the roots of this polynomial. Via the multiple equal-difference representations of the defining set of the generator polynomial of a simple-root constacyclic code, we obtain a family of upper bounds on its Hamming distance, among which the weakest one coincides with the Singleton bound, while the strongest one is defined to be the arithmetic Singleton bound for this code. Therefore the arithmetic Singleton bound is always stronger than the classical Singleton bound, and is in fact strictly stronger in numerous nontrivial cases. The arithmetic Singleton bound partially measures the restriction on the Hamming distance ofa simple-root constacyclic code imposed by its arithmetic structure. In particular, for an irreducible constacyclic code, the multiple equal-difference representations of the defining set of its generator polynomial are completely determined, via which the arithmetic Singleton bound is computed concretely. This is a joint work with Wu Hongfeng