On solving systems of random linear disequations

Understand

An important subcase of the hidden subgroup problem is equivalent to the shift problem over abelian groups.

• An efficient solution to the latter problem would serve as a building block of quantum hidden subgroup algorithms over solvable groups.
• The main idea of a promising approach to the shift problem is reduction to solving systems of certain random disequations in finite abelian groups.
• The random disequations are actually generalizations of linear functions distributed nearly uniformly over those not containing a specific group element in the kernel.