Bounds on Codes with Locality and Availability

S. B. Balaji; P. Vijay Kumar

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arXiv · 1611.00159

Bounds on Codes with Locality and Availability

S. B. Balaji·P. Vijay Kumar

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Abstract

In this paper we investigate bounds on rate and minimum distance of codes with $t$ availability. We present bounds on minimum distance of a code with $t$ availability that are tighter than existing bounds. For bounds on rate of a code with $t$ availability, we restrict ourselves to a sub-class of codes with $t$ availability called codes with strict $t$ availability and derive a tighter rate bound. Codes with strict $t$ availability can be defined as the null space of an $(m \times n)$ parity-check matrix $H$, where each row has weight $(r+1)$ and each column has weight $t$, with intersection between support of any two rows atmost one. We also present two general constructions for codes with $t$ availability.

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S. B. Balaji, P. Vijay Kumar. 2016-11-01. Bounds on Codes with Locality and Availability. https://arxiv.org/abs/1611.00159

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