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Efficient generation of binary words of given weight

  • Nicolas Sendrier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1025)

Abstract

We thus provide here a linear time encoder/decoder of binary sequences into words of given weight and length. Furthermore, our algorithm is easy to implement and requires a limited amount of memory. Any exact solution, that a bijection between Wn,t and {1,2,..., (n/t)} will require, as far as we know, an algorithm of complexity at least O(n2), and computations over large integers.

It must be noted however that the statistical properties of the words generated are not very good. The major drawback being that the average length of the last sequence of consecutive “0”s is much larger than the other. For instance with n=1024, t=50 and K=80 the length of this last sequence is 124 instead of 20.

Keywords

Linear Time Binary Sequence Efficient Generation Large Integer Information Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. G. Gallager. Information Theory and Reliable Communication. John Wiley & Sons, 1968.Google Scholar
  2. 2.
    H. Niederreiter. Knapsack-type cryptosystems and algebraic coding theory. Prob. Contr. Inform. Theory, 15(2):157–166, 1986.Google Scholar
  3. 3.
    V.M. Sidelnikov. A public-key cryptosystem based on Reed-Muller codes. Discrete Mathematics and Applications, 4(3):191–207, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Nicolas Sendrier
    • 1
  1. 1.INRIA, Domaine de Voluceau, RocquencourtLe Chesnay CedexFrance

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