A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Highly resilient correctors for polynomials
Information Processing Letters
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Fast encoding and decoding of Gabidulin codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Linear-Algebraic List Decoding of Folded Reed-Solomon Codes
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Optimal rate list decoding via derivative codes
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
A welch–berlekamp like algorithm for decoding gabidulin codes
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Linear authentication codes: bounds and constructions
IEEE Transactions on Information Theory
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
IEEE Transactions on Information Theory
Coding for Errors and Erasures in Random Network Coding
IEEE Transactions on Information Theory
A Rank-Metric Approach to Error Control in Random Network Coding
IEEE Transactions on Information Theory
List decoding reed-solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our construction is based on a variant of the folded Reed-Solomon codes in the world of linearized polynomials, and the algorithm is inspired by the recent linear-algebraic approach to list decoding [4]. Ours is the first list decoding algorithm for subspace codes that can handle deletions; even one deletion can totally distort the structure of the basis of a subspace and is thus challenging to handle. When there are only insertions, we also present results for list decoding subspace codes that are the linearized analog of Reed-Solomon codes (proposed in [15, 8], and closely related to the Gabidulin codes for rank-metric coding), obtaining some improvements over similar results in [10].