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N-Dimensional Binary Vector Spaces Cover
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|Jun 2013

References

  1. [1] Jesse Alama. The vector space of subsets of a set based on symmetric difference. FormalizedMathematics, 16(1):1-5, 2008. doi:10.2478/v10037-008-0001-7.10.2478/v10037-008-0001-7
  2. [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  3. [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  4. [4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  5. [5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  6. [6] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  7. [7] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. FormalizedMathematics, 1(3):529-536, 1990.
  8. [8] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  9. [9] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  10. [10] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  11. [11] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  12. [12] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  13. [13] X. Lai. Higher order derivatives and differential cryptoanalysis. Communications andCryptography, pages 227-233, 1994.10.1007/978-1-4615-2694-0_23
  14. [14] Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.
  15. [15] J.C. Moreira and P.G. Farrell. Essentials of Error-Control Coding. John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, 2006.
  16. [16] Hiroyuki Okazaki and Yasunari Shidama. Formalization of the data encryption standard. Formalized Mathematics, 20(2):125-146, 2012. doi:10.2478/v10037-012-0016-y.10.2478/v10037-012-0016-y
  17. [17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
  18. [18] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  19. [19] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  20. [20] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. FormalizedMathematics, 1(5):865-870, 1990.
  21. [21] Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1 (5):877-882, 1990.
  22. [22] Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990.
  23. [23] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  24. [24] Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.
  25. [25] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  26. [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  27. [27] Mariusz Zynel. The Steinitz theorem and the dimension of a vector space. FormalizedMathematics, 5(3):423-428, 1996.
DOI: https://doi.org/10.2478/forma-2013-0008 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 75 - 81
Published on: Jun 1, 2013
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2013 Kenichi Arai, Hiroyuki Okazaki, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 21 (2013): Issue 2 (June 2013)