List decoding group homomorphisms between supersolvable groups

We show that the set of homomorphisms between two supersolvable groups can be locally list decoded up to the minimum distance of the code, extending the results of Dinur et al who studied the case where the groups are abelian. Moreover, when specialized to the abelian case, our proof is more streamlined and gives a better constant in the exponent of the list size. The constant is improved from about 3.5 million to 105.

[1]  David Zuckerman,et al.  List-decoding reed-muller codes over small fields , 2008, STOC '08.

[2]  Cynthia Dwork,et al.  Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, May 17-20, 2008 , 2008, STOC.

[3]  Parikshit Gopalan,et al.  A Fourier-Analytic Approach to Reed–Muller Decoding , 2010, IEEE Transactions on Information Theory.

[4]  Madhu Sudan,et al.  Decodability of group homomorphisms beyond the johnson bound , 2008, STOC '08.

[5]  Shachar Lovett,et al.  List decoding Reed-Muller codes over small fields , 2014, Electron. Colloquium Comput. Complex..

[6]  Prasad Raghavendra,et al.  List decoding tensor products and interleaved codes , 2008, STOC '09.

[7]  Leonid A. Levin,et al.  A hard-core predicate for all one-way functions , 1989, STOC '89.

[8]  Madhu Sudan,et al.  Local Decoding and Testing for Homomorphisms , 2006, APPROX-RANDOM.

[9]  Venkatesan Guruswami,et al.  Optimal Rate List Decoding via Derivative Codes , 2011, APPROX-RANDOM.

[10]  Alan Guo.  Group Homomorphisms as Error Correcting Codes , 2015, Electron. J. Comb..

[11]  Venkatesan Guruswami,et al.  Linear-Algebraic List Decoding of Folded Reed-Solomon Codes , 2011, 2011 IEEE 26th Annual Conference on Computational Complexity.

[12]  Swastik Kopparty.  List-Decoding Multiplicity Codes , 2012, Theory Comput..

[13]  Venkatesan Guruswami,et al.  Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy , 2005, IEEE Transactions on Information Theory.