The enumeration of certain sets of block maps

نویسنده

  • Frank Rhodes
چکیده

An n-block is a sequence b, b,. b,, where b, E Z, for 1 < i < n, and an n-block map is a function from the set of n-blocks to the ring Z,. The n-block maps form the ring GF(2) {x,. x1,..., x, 1 xf = 1). The set of all block maps with the operations of addition and polynomial substitution form a near-ring. The general problem of searching non-linear block maps for factors with respect to polynomial substitution seems to be extremely complex. However, effective search procedures have been described for factors within certain sets of block maps which are non-linear but are linear in the first variable. In this paper we show that the smallest of these sets contains just over 85% of the block maps which are linear in the first variable. The largest of the sets, for which there is an additional step in the search procedure, contains over 99% of the block maps which are linear in the first variable. ‘Cl 1987

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عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 45  شماره 

صفحات  -

تاریخ انتشار 1987