Work

A classification of invariant sets of constant-weight tuples and applications to covering schemes

Year: 2026

Type: article

Abstract: Covering schemes were recently introduced as a generalization of both difference matrices and difference schemes, providing an efficient method for building covering arrays with a certain degree of symmetry. On the other hand, Tang and Woo (1983) showed that sets of constant-weight tuples yield several upper bounds on covering arrays. However, these sets usually do not have enough symmetry to induce good covering schemes. In this work, we derive a classification of invariant sets of constant-weight tuples under the action of the diagonal group of $$\mathbb {Z}_q^k$$ . This classification enables us to obtain new upper bounds on covering scheme numbers, including the exact class for binary covering scheme numbers with k columns and strength $$k-2.$$

Source: Cryptography and Communications

DOI: 10.1007/s12095-026-00890-2

Authors: André G. Castoldi, Anderson N. Martinhão, Emerson L. Monte Carmelo, Pablo H. Perondi, Otávio J. N. T. N. dos Santos

Institutions: Universidade Tecnológica Federal do Paraná, Universidade Federal da Grande Dourados, Universidade Estadual de Maringá, Universidade Estadual de Mato Grosso do Sul

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Universidade Estadual de Maringá