Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields

2021/06/12 by Peter J. Dukes, Dukes, Peter J., Xavier Martínez-Rivera +1
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Advanced Wireless Communication Techniques

paper · pdf · doi:10.48550/arxiv.2106.06756

Abstract

The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ \mathbbF^{n × n} is defined as ℓ₁ ℓ₂ ⋯ ℓ_n, where ℓ_j ∈ \\ttA, \ttS, \ttN\ according to whether all, some but not all, or none of the principal minors of order j of B are nonzero. Building upon the second author's recent classification of the epr-sequences of symmetric matrices over the field \mathbbF=\mathbbF₂, we initiate a study of the case \mathbbF=\mathbbF₃. Moreover, epr-sequences over finite fields are shown to have connections to Ramsey theory and coding theory.

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