Multiply Constant-Weight Codes and the Reliability of Loop Physically Unclonable Functions

TL;DR

This paper introduces multiply constant-weight codes to enhance the reliability of PUF responses, extending classical coding techniques and analyzing their bounds, rates, and asymptotic properties.

Contribution

It develops a new class of codes, derives Johnson bounds for them, and compares their rates to existing constant-weight codes, with asymptotic analysis.

Findings

Johnson bounds are asymptotically tight under certain conditions.

Multiply constant-weight codes have the same rates as constant-weight codes of similar parameters.

Asymptotic analysis confirms the efficiency of the new code constructions.

Abstract

We introduce the class of multiply constant-weight codes to improve the reliability of certain physically unclonable function (PUF) response. We extend classical coding methods to construct multiply constant-weight codes from known $q$-ary and constant-weight codes. Analogues of Johnson bounds are derived and are shown to be asymptotically tight to a constant factor under certain conditions. We also examine the rates of the multiply constant-weight codes and interestingly, demonstrate that these rates are the same as those of constant-weight codes of suitable parameters. Asymptotic analysis of our code constructions is provided.