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Electronic Colloquium on Computational Complexity

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Reports tagged with Johnson bound:
TR06-020 | 10th February 2006
Akinori Kawachi, Tomoyuki Yamakami

Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding

Revisions: 1

We present three new quantum hardcore functions for any quantum one-way function. We also give a "quantum" solution to Damgard's question (CRYPTO'88) on his pseudorandom generator by proving the quantum hardcore property of his generator, which has been unknown to have the classical hardcore property.
Our technical tool is ... more >>>

TR08-105 | 26th November 2008
Parikshit Gopalan, Venkatesan Guruswami, Prasad Raghavendra, Prasad Raghavendra

List Decoding Tensor Products and Interleaved Codes

We design the first efficient algorithms and prove new combinatorial bounds for list decoding tensor products of codes and interleaved codes.

1)We show that for every code, the ratio of its list decoding radius to its minimum distance stays unchanged under the tensor product operation (rather than squaring, as one ... more >>>

TR13-140 | 8th October 2013
Atri Rudra, Mary Wootters

Every list-decodable code for high noise has abundant near-optimal rate puncturings

We show that any $q$-ary code with sufficiently good distance can be randomly punctured to obtain, with high probability, a code that is list decodable up to radius $1 - 1/q - \epsilon$ with near-optimal rate and list sizes.

Our results imply that ``most" Reed-Solomon codes are list decodable ... more >>>

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