Joan Boyar, rene peralta

We consider the problem of computing the Hamming weight of an n-bit vector using a circuit with gates for GF2 addition and multiplication only. We show the number of multiplications necessary and sufficient to build such a circuit is n - |n| where |n| is the Hamming weight of the ... more >>>

Vikraman Arvind, Sebastian Kuhnert, Johannes Köbler, Jacobo Toran

Given a system of linear equations $Ax=b$ over the binary field $\mathbb{F}_2$ and an integer $t\ge 1$, we study the following three algorithmic problems:

1. Does $Ax=b$ have a solution of weight at most $t$?

2. Does $Ax=b$ have a solution of weight exactly $t$?

3. Does $Ax=b$ have a ...
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