Exponential sums and rank of double persymmetric matrices over F_2

TL;DR

This paper derives explicit formulas for counting double persymmetric matrices over F_2 with a specified rank using exponential quadratic sums, advancing understanding of their structural properties.

Contribution

It introduces a novel method employing exponential quadratic sums to explicitly count double persymmetric matrices of given rank over F_2.

Findings

Explicit formulas for the number of double persymmetric matrices of given rank

Application of exponential quadratic sums in matrix enumeration

Enhanced understanding of matrix rank distribution over F_2

Abstract

We obtain, using exponential quadratic sums, explicit expressions for the number of double persymmetric matrices with entries in F_2 of given rank. (A matix [a(i,j)) is persymmetric if a(i,j) = a(r,s) for i+j = r+s)