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Paper:

TR22-012 | 2nd February 2022 00:26

On List Decoding Transitive Codes From Random Errors

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TR22-012
Authors: Anup Rao, Oscar Sprumont
Publication: 2nd February 2022 00:26
Downloads: 158
Keywords: 


Abstract:

We study the error resilience of transitive linear codes over $F_2$. We give tight bounds on the weight distribution of every such code $C$, and we show how these bounds can be used to infer bounds on the error rates that $C$ can tolerate on the binary symmetric channel. Using this connection, we show that every transitive code can be list-decoded from random errors. As an application, our results imply list-decoding bounds for Reed-Muller codes even when the rate exceeds the channel capacity.



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