On Zero Skip-Cost Generalized Fractional-Repetition Codes from Covering Designs

TL;DR

This paper investigates zero skip-cost generalized fractional repetition codes derived from covering designs, demonstrating their attainability with or without expansion, and providing multiple constructions and theoretical proofs.

Contribution

It introduces methods to construct zero skip-cost fractional repetition codes from covering designs, including explicit constructions and non-constructive proofs of their existence without expansion.

Findings

Zero skip-cost codes are always attainable from covering designs.

Explicit constructions of such codes are provided.

No expansion is needed for large covering systems.

Abstract

We study generalized fractional repetition codes that have zero skip cost, and which are based on covering designs. We show that a zero skip cost is always attainable, perhaps at a price of an expansion factor compared with the optimal size of fractional repetition codes based on Steiner systems. We provide three constructions, as well as show non-constructively, that no expansion is needed for all codes based on sufficiently large covering systems.