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   In this paper the theory and design of codes capable of correcting t insertion/deletion of the symbol 0 in each and every bucket of zeros (i. e., zeros in between two consecutive ones) are studied. It is shown that this problem is related to the zero error capacity achieving codes in limited magnitude error channel. Close to optimal non-systematic code designs and the encoding/decoding algorithms are described. 

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   A powerful feature in mechanism design is the ability to irrevocably commit to the rules of a mechanism. Commitment is achieved by public declaration, which enables players to verify incentive properties in advance and the outcome in retrospect. However, public declaration can reveal superfluous information that the mechanism designer might prefer not to disclose, such as her target function or private costs. Avoiding this may be possible via a trusted mediator; however, the availability of a trustworthy mediator, especially if mechanism secrecy must be maintained for years, might be unrealistic. We propose a new approach to commitment, and show how to commit to, and run, any given mechanism without disclosing it, while enabling the verification of incentive properties and the outcome—all without the need for any mediators. Our framework is based on zero-knowledge proofs—a cornerstone of modern cryptographic theory. Applications include both private-type settings such as auctions and private-action settings such as contracts, as well as non-mediated bargaining with hidden yet binding offers. 

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   Zimmer, Margaret A.; Kaiser, Kendra E.; Blaszczak, Joanna R.; Zipper, Samuel C.; Hammond, John C.; Fritz, Ken M.; Costigan, Katie H.; Hosen, Jacob; Godsey, Sarah E.; Allen, George H.; et al (May 2020, WIREs Water)