Exponential sums and rank of triple persymmetric matrices over F_2

TL;DR

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

Contribution

It introduces a novel method employing exponential quadratic sums to explicitly enumerate triple persymmetric matrices over F_2 by rank.

Findings

Explicit formulas for counting matrices of given rank

Use 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 triple persymmetric matrices over F_2 of given rank. (A matrix [a(i,j)] is persymmetric if a(i,j) = a(r,s) for i+j = r+s)