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Finding an asymptotically bad family of $q$th power residue codes
1.  The University of Texas at Austin, Mathematics Department, C1200, 1 University Station, Austin, TX, 78712, United States 
In this paper, we examine families of generalized binary quadratic residue codes, named $q$th power residue codes, where $q$ is a fixed odd prime, and find an asymptotically bad subfamily of these codes. For each prime $l$ we will construct a $q$th power residue code of length $p$ (determined by our choice of $l$ ) and minimal distance $d_p$, with the property that as $l$ approaches infinity, $p$ also tends towards infinity, and $\lim_{l to \infty} \frac{d_p}{p} = 0$.
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