A Characterization of q-binomials and its Application to Coding Theory
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We present a new perspective on q-binomials, also known as Gaussian binomial coefficients. This new perspective, which is the main theorem of the paper, relates q-binomials to a type of generating function. The theorem may be applied to determine cardinalities of certain error-correcting codes based on Varshamov-Tenengolts codes. This application is related to a problem previously studied by R. P. Stanley.
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