Families of twisted tensor product codes

TL;DR

This paper introduces new families of error-correcting codes derived from geometric properties of certain algebraic varieties and spreads in projective spaces, with exact parameters and minimum weight characterization.

Contribution

It develops a novel construction of constacyclic codes using twisted tensor products and geometric methods, providing explicit parameters and weight distribution.

Findings

Exact parameters of the new codes are determined.

Words of minimum weight are characterized.

Several families of constacyclic codes are introduced.

Abstract

Using geometric properties of the variety $\cV_{r,t}$, the image under the Grassmannian map of a Desarguesian $(t-1)$-spread of $\PG(rt-1,q)$, we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We exactly determine the parameters of these codes and characterise the words of minimum weight.