2022/07/13 by Ryan Curry, R. Amzi Jeffs, Curry, Ryan +5
Computer Science · #Coding theory and cryptography #Advanced Data Storage Technologies #Cryptography and Data Security
paper · pdf · doi:10.48550/arxiv.2207.06266
We prove algebraic and combinatorial characterizations of the class of inductively pierced codes, resolving a conjecture of Gross, Obatake, and Youngs. Starting from an algebraic invariant of a code called its canonical form, we explain how to compute a piercing order in polynomial time, if one exists. Given a piercing order of a code, we explain how to construct a realization of the code using a well-formed collection of open balls, and classify the minimal dimension in which such a realization exists.