The structure of quaternary quantum caps

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• 作者：Jürgen Bierbrauer (1)
  Daniele Bartoli (2)
  Giorgio Faina (2)
  Stefano Marcugini (2)
  Fernanda Pambianco (2)
  Yves Edel (3)
  
• 关键词：Quantum cap ; Quaternary code ; Quantum stabilizer code ; Symplectic geometry ; Projective space ; Trace ; Hyperoval ; Elliptic quadric ; 11T71 ; 51E22 ; 81P70
• 刊名：Designs, Codes and Cryptography
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：72
• 期：3
• 页码：733-747
• 全文大小：
• 参考文献：1. Bartoli D., Bierbrauer J., Marcugini S., Pambianco F.: Geometric Constructions of Quantum Codes, Error-Correcting Codes, Finite Geometries and Cryptography, Contemporary Mathematics, vol. 523, pp. 149-54. American Mathematical Society, Providence (2010).
  2. Bartoli D., Davydov A.A., Marcugini S., Pambianco F.: The minimum order of complete caps in \(PG(4,4)\) . Advanc. Math. Commun. 5, 37-0 (2011).
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  18. Yu S., Bierbrauer J., Dong Y., Chen Q., Oh C.H.: All the stabilizer codes of distance \(3\) . IEEE Trans. Inf. Theory to appear.
  
• 作者单位：Jürgen Bierbrauer (1)
  Daniele Bartoli (2)
  Giorgio Faina (2)
  Stefano Marcugini (2)
  Fernanda Pambianco (2)
  Yves Edel (3)
  
  1. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA
  2. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy
  3. Department of Mathematics, Ghent University, Ghent, Belgium
  
• ISSN：1573-7586

文摘

We give a geometric description of binary quantum stabilizer codes. In the case of distance \(d=4\) this leads to the notion of a quaternary quantum cap. We describe several recursive constructions for quantum caps, determine the quantum caps in \(PG(3,4)\) and the cardinalities of quantum caps in \(PG(4,4).\)