GAUSS Seminar

Speaker:

Yariana Diaz

Topic:

Optimal Batch Properties of Hamming and Reed-Muller Codes

$Batch codes, introduced by Ishai et al., encode a string x ∈ Σ^k into an m-tuple of strings, called buckets. In this paper we consider multiset batch codes wherein a set of t users wish to access one bit of information each from the original string. We introduce a concept of optimal batch codes. We first show that binary Hamming codes are optimal batch codes. The main body of this work provides batch properties of Reed-Muller codes. We look at locality and availability properties of first order Reed-Muller codes over any finite field. We then show that binary first order Reed-Muller codes are optimal batch codes when the number of users is 4 and generalize our study to the family of binary Reed-Muller codes which have order less than half their length.$

Event Date:

April 27, 2022 - 4:30pm to 5:20pm

Location:

SH 137 and Online (see URL)

URL:

https://uiowa.zoom.us/j/96851047768?pwd=SkFEY0c4a1IvNWZWS2laWGs1aUcydz09

Host:

Manny Albrizzio & Garrett Mason

Calendar Category:

Seminar

Seminar Category:

GAUSS