The number of linearly independent binary vectors with applications to the construction of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes
نویسندگان
چکیده
We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1 ≤ k ≤ n. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes. 1991 AMS(MOS) Classification: Primary: 11T30; secondary: 05B15.
منابع مشابه
A Family of Binary (t, m, s)-Nets of Strength 5
t, m, s)−nets were defined by Niederreiter [6], based on earlier work by Sobol’ [7], in the context of quasi-Monte Carlo methods of numerical integration. Formulated in combinatorial/coding theoretic terms a binary linear (m − k,m, s)2-net is a family of ks vectors in F2 satisfying certain linear independence conditions (s is the length, m the dimension and k the strength: certain subsets of k ...
متن کاملSome Optimal Codes From Designs
The binary and ternary codes spanned by the rows of the point by block incidence matrices of some 2-designs and their complementary and orthogonal designs are studied. A new method is also introduced to study optimal codes.
متن کاملAssociation Schemes for Ordered Orthogonal Arrays and (t,m,s)-nets
In an earlier paper 9], we studied a generalized Rao bound for ordered orthogonal arrays and (T; M; S)-nets. In this paper, we extend this to a coding-theoretic approach to ordered orthogonal arrays. Using a certain association scheme, we prove a MacWilliams-type theorem for linear ordered orthogonal arrays and linear ordered codes as well as a linear programming bound for the general case. We ...
متن کاملUmbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms
We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...
متن کاملLinear Programming Bounds for Ordered Orthogonal Arrays and (T;M;S)-nets
A recent theorem of Schmid and Lawrence establishes an equivalence between (T; M; S)-nets and ordered orthogonal arrays. This leads naturally to a search both for constructions and for bounds on the size of an ordered orthogonal array. Subsequently, Martin and Stinson used the theory of association schemes to derive such a bound via linear programming. In practice, this involves large-scale com...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006