# On optimal weak algebraic manipulation detection codes and weighted external difference families

## TL;DR

This paper characterizes weak AMD codes using generalized external difference families, improves bounds on tampering success probabilities, and proposes explicit constructions for optimal codes.

## Contribution

It introduces a combinatorial characterization of weak AMD codes via BSWEDFs and provides new constructions for optimal weak AMD codes.

## Key findings

- Improved lower bound on tampering success probability.
- Established relationship between weak AMD codes and BSWEDFs.
- Provided explicit constructions for optimal weak AMD codes.

## Abstract

This paper provides a combinatorial characterization of weak algebraic manipulation detection (AMD) codes via a kind of generalized external difference families called bounded standard weighted external difference families (BSWEDFs). By means of this characterization, we improve a known lower bound on the maximum probability of successful tampering for the adversary's all possible strategies in weak AMD codes. We clarify the relationship between weak AMD codes and BSWEDFs with various properties. We also propose several explicit constructions for BSWEDFs, some of which can generate new optimal weak AMD codes.