Abstract: Data storage techniques and solutions simultaneously provide efficient random access to information and high noise resilience. The amount of storage space utilized is only slightly larger than the size of the data. The solution is based on locally decodable error-correcting codes (also referred to as locally decodable codes or LDCs). Locally decodable codes are described herein that are more efficient than conventional locally decodable codes. Such locally decodable codes are referred to as “multiplicity codes”. These codes are based on evaluating multivariate polynomials and their derivatives. Multiplicity codes extend traditional multivariate polynomial based (e.g., Reed-Muller) codes. Multiplicity codes inherit the local decodability of Reed-Muller codes, and at the same time achieve substantially better parameters.

Abstract: Data storage techniques and solutions simultaneously provide efficient random access to information and high noise resilience. The amount of storage space utilized is only slightly larger than the size of the data. The solution is based on locally decodable error-correcting codes (also referred to as locally decodable codes or LDCs). Locally decodable codes are described herein that are more efficient than conventional locally decodable codes. Such locally decodable codes are referred to as “multiplicity codes”. These codes are based on evaluating multivariate polynomials and their derivatives. Multiplicity codes extend traditional multivariate polynomial based (e.g., Reed-Muller) codes. Multiplicity codes inherit the local decodability of Reed-Muller codes, and at the same time achieve substantially better parameters.