Random Oper. & Stock Eqs., Vol. 1, No. 3, pp. 287-292 (1993) O VSP 1993 The asymptotics of the number of fc-dimensional subspaces of minimal weight over a finite field V. I. MASOL Department of Mechanics and Mathematics, Kyjiv University, 25201 7 Kyjiv, Ukraine Received for ROSE 25 May 1992 Abstract--Prom the totality of ^-dimensional subspaces of an -dimensional vector space over a finite field, one subspace is chosen randomly. The asymptotical behaviour (n --> oo) of the probability that this subspace will be of minimal weight is established. It is well known  that the number of fc-dimensional subspaces V* in the n-dimensional vector space Vn over a finite field GF(q) which consists of q elements (q is a degree of a prime number) is - ("-* -W'' -O· jsQ (l) Let ] =1, n ^ 0. The number of non-zero components of the vector v E Vn is said to be the weight of the vector v. The minimal weight of a non-zero vector v £ V* is called the weight of thefc-dimensionalsubspace V* of the space Vn, l ^ k ^ n. Later on ^*|w) denotes the - dimensional subspace of weight w, V(*|u;) !
Random Operators and Stochastic Equations – de Gruyter
Published: Jan 1, 1993
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