An upper bound of Singleton type for componentwise products of linear codes

TL;DR

This paper establishes an upper bound on the minimum weight of componentwise products of linear codewords, generalizing the Singleton bound and linking it to code dimensions.

Contribution

It introduces a new upper bound for the minimum weight of componentwise products of linear codes, extending the classical Singleton bound.

Findings

The bound relates the minimum weight to code dimensions.

It generalizes the classical Singleton bound.

Provides theoretical limits for code product weights.

Abstract

We give an upper bound that relates the minimum weight of a nonzero componentwise product of codewords from some given number of linear codes, with the dimensions of these codes. Its shape is a direct generalization of the classical Singleton bound.