Direct products in projective Segre codes
Azucena Tochimani, Maria Vaz Pinto, Rafael H. Villarreal
TL;DR
This paper introduces projective Segre codes, a new family of codes constructed as direct products of projective Reed-Muller-type codes, and analyzes their parameters using algebraic methods.
Contribution
It presents the first study of projective Segre codes and demonstrates their structure as direct products of known codes, extending understanding of Reed-Muller-type codes.
Findings
Projective Segre codes are direct products of Reed-Muller-type codes.
The paper recovers existing results on codes over Segre varieties.
Basic parameters of these codes are characterized using algebraic techniques.
Abstract
Let K=Fq be a finite field. We introduce a family of projective Reed-Muller-type codes called projective Segre codes. Using commutative algebra and linear algebra methods, we study their basic parameters and show that they are direct products of projective Reed-Muller-type codes. As a consequence we recover some results on projective Reed-Muller-type codes over the Segre variety and over projective tori.
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