@MISC{NBVECTSP.MIZ,
  AUTHOR = {Arai, Kenichi and Okazaki, Hiroyuki},
  TITLE = {$n$-dimensional Binary Vector Spaces},
  DAY = {17},
  MONTH = {April},
  YEAR = {2013},
  ADDRESS1 = {Tokyo University of Science, Chiba, Japan},
  ADDRESS2 = {Shinshu University, Nagano, Japan},
  SUMMARY = {The binary set $\{0,1\}$ together with modulo-2 addition
    and multiplication is called a binary field, which is denoted by
    $\mathbb{F}_2$. The binary field $\mathbb{F}_2$ is defined in
    \cite{BSPACE.ABS}. A vector space over $\mathbb{F}_2$ is called a
    binary vector space. The set of all binary vectors of length $n$
    forms an $n$-dimensional vector space $V_n$ over $\mathbb{F}_2$.
    Binary fields and $n$-dimensional binary vector spaces play
    an important role in practical computer science, for example, coding
    theory \cite{ECC:2006} and cryptology. In cryptology, binary fields
    and $n$-dimensional binary vector spaces are very important in
    proving the security of cryptographic systems \cite{Lai1994}.
    In this article, we define the $n$-dimensional binary vector
    space $V_n$. Moreover, we formalize some facts about the
    $n$-dimensional binary vector space $V_n$.}}

@BOOK{ECC:2006,
  AUTHOR = {J.C. Moreira and P.G. Farrell},
  TITLE = {Essentials of Error-Control Coding},
  PUBLISHER = {John Wiley \& Sons Ltd, The Atrium, Southern Gate,
Chichester},
  YEAR = {2006}}

@ARTICLE{Lai1994,
  AUTHOR = {X. Lai},
  TITLE = {Higher Order Derivatives and Differential Cryptoanalysis},
  JOURNAL = {Communications and Cryptography},
  PAGES = {227--233},
  PUBLISHER = {Kluwer Academic Publishers},
  YEAR = {1994}}

