The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Generators and irreducible polynomials over finite fields
Mathematics of Computation
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximating the SVP to within a factor (1+1/dimE) is NP-Hard under randomized reductions
Journal of Computer and System Sciences
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
SIAM Journal on Computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Hardness of approximating the shortest vector problem in lattices
Journal of the ACM (JACM)
Tensor-based hardness of the shortest vector problem to within almost polynomial factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the List and Bounded Distance Decodability of Reed-Solomon Codes
SIAM Journal on Computing
Complexity of Decoding Positive-Rate Reed-Solomon Codes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
Hardness of approximating the minimum distance of a linear code
IEEE Transactions on Information Theory
A simple deterministic reduction for the gap minimum distance of code problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Stopping set distributions of algebraic geometry codes from elliptic curves
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
On the minimum degree up to local complementation: bounds and complexity
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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Determining the minimum distance of a linear code is one of the most important problems in algorithmic coding theory. The exact version of the problem was shown to be NP-complete in [14]. In [8], the gap version of the problem was shown to be NP-hard for any constant factor under a randomized reduction. It was shown in the same paper that the minimum distance problem is not approximable in randomized polynomial time to the factor 2log1-ε n unless NP ⊆ RTIME(2polylog(n)). In this paper, we derandomize the reduction and thus prove that there is no deterministic polynomial time algorithm to approximate the minimum distance to any constant factor unless P=NP. We also prove that the minimum distance is not approximable in deterministic polynomial time to the factor 2log1-εn unless NP ⊆ DTIME(2polylog(n)). As the main technical contribution, for any constant 2/3