Separating partition systems and locally different sequences
SIAM Journal on Discrete Mathematics
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
A characterization of span program size and improved lower bounds for monotone span programs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On codes with the identifiable parent property
Journal of Combinatorial Theory Series A
List decoding algorithms for certain concatenated codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Guessing secrets with inner product questions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Guessing secrets efficiently via list decoding
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Coding Theory
Journal of Combinatorial Theory Series A
A Hypergraph Approach to the Identifying Parent Property: The Case of Multiple Parents
SIAM Journal on Discrete Mathematics
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Efficient decoding of Reed-Solomon codes beyond half the minimum distance
IEEE Transactions on Information Theory
Two cooperative versions of the Guessing Secrets problem
Information Sciences: an International Journal
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We consider the guessing secrets problem defined by Chung et al. [2001]. This is a variant of the standard 20 questions game where the player has a set of k 1 secrets from a universe of N possible secrets. The player is asked Boolean questions about the secret. For each question, the player picks one of the k secrets adversarially, and answers according to this secret. We present an explicit set of O(log N) questions together with an efficient (i.e., poly(log N) time) algorithm to solve the guessing secrets problem for the case of 2 secrets. This answers the main algorithmic question left unanswered by Chung et al. [2001]. The main techniques we use are small &epsis;-biased spaces and the notion of list decoding. We also establish bounds on the number of questions needed to solve the k-secrets game for k 2, and discuss how list decoding can be used to get partial information about the secrets, specifically to find a small core of secrets that must intersect the actual set of k secrets.