A Construction of Maximally Recoverable Codes With Order-Optimal Field Size
Han Cai, Ying Miao, Moshe Schwartz, Xiaohu Tang
Abstract
We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic regimes, the constructed codes have order-optimal alphabet size, asymptotically matching the known lower bound.
Topics & Concepts
MathematicsAlphabetBlock codeExpander codeLinear codeField sizeFinite fieldDiscrete mathematicsUpper and lower boundsTornado codeOrder (exchange)Reed–Muller codeReed–Solomon error correctionAlgorithmDecoding methodsPhysicsPhilosophyFinanceEconomicsOpticsMathematical analysisLinguisticsImaging phantomAdvanced Data Storage TechnologiesCellular Automata and ApplicationsCoding theory and cryptography