Group homomorphisms as error correcting codes

We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups $G$ and $H$. We prove some general structural results on how the distance behaves with respect to natural group operations, such as passing to subgroups and quotients, and taking products. Our main result is a general formula for the distance when $G$ is solvable or $H$ is nilpotent, in terms of the normal subgroup structure of $G$ as well as the prime divisors of $|G|$ and $|H|$. In particular, we show that in the above case, the distance is independent of the subgroup structure of $H$. We complement this by showing that, in general, the distance depends on the subgroup structure $G$.Comment: 13 page

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.Comment: 11 page

Optimal Dynamic Nonlinear Income Taxation under Loose Commitment

This paper examines an infinite-horizon model of dynamic nonlinear income taxation in which there exists a small probability that the government cannot commit to its future tax policy. In this "loose commitment" environment, we find that even a little uncertainty over whether the government can commit yields substantial effects on the optimal dynamic nonlinear income tax system. Under an empirically plausible parameterization, numerical simulations show that high-skill individuals must be subsidized in the short run, despite the government's redistributive objective, unless the probability of commitment is higher than 98%. Loose commitment also reverses the short-run welfare effects of changes in most model parameters. In particular, all individuals are worse-off, rather than better-off, in the short run when the proportion of high-skill individuals in the economy increases. Finally, our main findings remain qualitatively robust to a setting in which loose commitment is modelled as a Markov switching process.Dynamic Income Taxation, Loose Commitment