On the Probability That a T-subset of a Nite Vector Space Contains an R-subspace{with Applications to Short, Light Codewords in a Bch Code
نویسنده
چکیده
Motivated by the problem of nding light (i.e., low weight) and short (i.e., low degree) codewords in narrow-sense, primitive BCH codes we consider the problem of determining the probability that a random t-set of vectors in an n dimensional vector space over GF (q) contains an r-dimensional subspace (or aane subspace). We nd some bounds for this and similar probabilities and apply these techniques to estimate how short a minimum weight codeword can be in a narrow-sense BCH code.
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