Direct products in projective Segre codes

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• 作者：Azucena Tochimani^a ; ^{tochimani@math.cinvestav.mx" class="auth_mail" title="E-mail the corresponding author} ; Maria Vaz Pinto^b ; ^{vazpinto@math.ist.utl.pt" class="auth_mail" title="E-mail the corresponding author} ; Rafael H. Villarreal^a ; ^{vila@math.cinvestav.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 13P25 ; secondary ; 15A78 ; 14G50 ; 11T71 ; 94B27 ; 94B05
• 刊名：Finite Fields and Their Applications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：39
• 期：Complete
• 页码：96-110
• 全文大小：392 K

文摘

Let K=F_q$K={\mathbb{F}}_q$ 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.