题目：Moore exponent sets and MRD codes

报告人: 周悦副研究员, 国防科技大学

Abstract: Let n be a positive integer and I a k-subset of integers in [0,n-1]. Given a k-tuple

,

let MA,I denote the matrix  with 0 i k-1 and j I. When I={0,1,..., k-1}, MA,I is called a Moore matrix which was introduced by E. H. Moore in 1896. It is well known that the determinant of a Moore matrix equals 0 if and only if ,...,   are Fq-linearly dependent. We call I that satisfies this property a Moore exponent set.

Moore exponent sets correspond to a special class of maximum rank-distance (MRD, for short) codes consisting of square matrices over finite fields. In fact, I={0,d,..., (k-1)d} is a Moore exponent set for any q and n with gcd(n,d)=1. It corresponds to the an important family of maximum rank-distance codes, which are usually called Delsarte-Gabidulin codes discovered by Delsarte (1978) and Gabidulin (1985) independently.

In this talk, we first summarize recent progresses in the construction of MRD codes and their equivalence problem. Then we turn to a special type of MRD codes which are equivalent to Moore exponent sets. We prove that I={0,1,3} is also a Moore exponent set for odd q and n=7. By using algebraic geometry approach, we also present an asymptotic classification result of them.

时间：4月12日（周五）上午11:10--12:00

地点：首都师大新教2楼   613 教室

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