Abstract
<p>Consider a set of vectors, <em>L</em>, which consists of vectors whose coordinates are 0 or 1. We find explicit formulas that counts the number of lattice paths from origin to (<em>a</em>,<em>b</em>,<em>c</em>,<em>d</em>) for using vectors in {(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)} ∪ <em>L</em> for various choices of <em>L</em>. In some cases we also give the recursive formulas for the same problem. Next we determine the minimum number of vectors that must be used to reach (<em>a</em>,<em>b</em>,<em>c</em>,<em>d</em>), also called the minimum distance problem, for different sets of vectors.</p>
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