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PublicationA Complete Classification of Partial-MDS (Maximally Recoverable) Codes Correcting one Additional Erasure( 2017-06-07)Partial-MDS (PMDS) codes are a family of locally repairable codes, mainly used for distributed storage. They are defined to be able to correct any pattern of s additional erasures, after a given number of erasures per locality group have occurred. This makes them also maximally recoverable (MR) codes, another class of locally repairable codes. It is known that MR codes in general, and PMDS codes in particular, exist for any set of parameters, if the field size is large enough. Moreover, some explicit constructions of PMDS codes are known, mostly with a strong restriction on the number of erasures that can be corrected per locality group. In this talk we give a general construction of PMDS codes that can correct any number of erasures per locality group, with the restriction s = 1, i.e., only one additional erasure can be corrected. Furthermore, we show that all PMDS codes for the given parameters are of this form, i.e., we give a classification of these codes. This implies a necessary and sufficient condition on the underlying field size for the existence of these codes (assuming that the MDS conjecture is true). This bound on the field size is in general much smaller than the previously known ones.Type: conference lecture
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PublicationA general model of boundedly rational observational learning: theory and evidence( 2016)Mueller-Frank, ManuelType: conference lecture
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PublicationAn Introduction to Code-Based Cryptography( 2023)These lecture notes provide an introduction to code-based cryptography, delving into the mathematical underpinnings of such systems and the challenges associated with designing secure yet practical schemes. We explore the main ideas of code-based public key encryption schemes and the strategies employed to potentially breach these cryptographic systems.Type: conference lecture
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