he Generalized Covering Radii of Linear Code

Autor(es)

Elimelech, Dor ^[1] ; Firer, Marcelo ^[2] ; Schwartz, Moshe ^[1]

Afiliação do(s) autor(es)

^[1] Ben Gurion Univ Negev, Sch Elect & Comp Engn, IL-8410501 Beer Sheva - Israel

^[2] Univ Estadual Campinas, Inst Math Stat & Sci Comp, BR-13083859 Campinas - Brazil

• Tipo de documento: Artigo Científico
• Fonte: IEEE TRANSACTIONS ON INFORMATION THEORY; v. 67, n. 12, p. 8070-8085, DEC 2021.
• Citações Web of Science: 0

Resumo

Motivated by an application to database linear querying, such as private information-retrieval protocols, we suggest a fundamental property of linear codes- the generalized covering radius. The generalized covering-radius hierarchy of a linear code characterizes the trade-off between storage amount, latency, and access complexity, in such database systems. Several equivalent definitions are provided, showing this as a combinatorial, geometric, and algebraic notion. We derive bounds on the code parameters in relation with the generalized covering radii, study the effect of simple code operations, and describe a connection with generalized Hamming weights. (AU)

• Processo FAPESP: 13/25977-7 - Segurança e confiabilidade da informação: teoria e prática
• Beneficiário: Marcelo Firer
• Modalidade de apoio: Auxílio à Pesquisa - Temático