Additive semisimple multivariable codes over ${\mathbb{F}_4}$

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• 作者：E. Martínez-Moro (1)
  A. Pi?era-Nicolás (1)
  I. F. Rúa (2)
  
• 关键词：Additive multivariable codes ; Abelian codes ; Quantum codes ; Duality ; 11T61 ; 94B99 ; 81P70 ; 13M10
• 刊名：Designs, Codes and Cryptography
• 出版年：2013
• 出版时间：November 2013
• 年：2013
• 卷：69
• 期：2
• 页码：161-180
• 全文大小：489KB
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• 作者单位：E. Martínez-Moro (1)
  A. Pi?era-Nicolás (1)
  I. F. Rúa (2)
  
  1. Institute of Mathematics (IMUVa) and Applied Mathematics Department, Universidad de Valladolid, Valladolid, Spain
  2. Departamento de Matemáticas, Universidad de Oviedo, Oviedo, Spain
  

文摘

The structure of additive multivariable codes over ${\mathbb{F}_4}$ (the Galois field with 4 elements) is presented. The semisimple case (i.e., when the defining polynomials of the code have no repeated roots) is specifically addressed. These codes extend in a natural way the abelian codes, of which additive cyclic codes of odd length are a particular case. Duality of these codes is also studied.