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Batch codes, introduced by Ishai et al. encode a string $x \in \Sigma^{k}$into an $m$-tuple of strings, called buckets. In this paper we considermultiset batch codes wherein a set of $t$-users wish to access one bit ofinformation each from the original string. We introduce a concept of optimalbatch codes. We first show that binary Hamming codes are optimal batch codes.The main body of this work provides batch properties of Reed-M\"uller codes. Welook at locality and availability properties of first order Reed-M\"uller codesover any finite field. We then show that binary first order Reed-M\"uller codesare optimal batch codes when the number of users is 4 and generalize our studyto the family of binary Reed-M\"uller codes which have order less than halftheir length.

Batch Codes from Hamming and Reed-M\"uller Codes