IRC +10216 is the prototypical carbon star exhibiting an extended molecular circumstellar envelope. Its spectral properties are therefore the template for an entire class of objects. The main goal is to systematically study the $lambda$ $sim$1.3 cm spectral line characteristics of IRC +10216. We carried out a spectral line survey with the Effelsberg-100 m telescope toward IRC +10216. It covers the frequency range between 17.8 GHz and 26.3 GHz (K-band). In the circumstellar shell of IRC +10216, we find 78 spectral lines, among which 12 remain unidentified. The identified lines are assigned to 18 different molecules and radicals. A total of 23 lines from species known to exist in this envelope are detected for the first time outside the Solar System and there are additional 20 lines first detected in IRC +10216. The potential orgin of U lines is also discussed. Assuming local thermodynamic equilibrium (LTE), we then determine rotational temperatures and column densities of 17 detected molecules. Molecular abundances relative to H$_{2}$ are also estimated. A non-LTE analysis of NH$_{3}$ shows that the bulk of its emission arises from the inner envelope with a kinetic temperature of 70$pm$20 K. Evidence for NH$_{3}$ emitting gas with higher kinetic temperature is also obtained, and potential abundance differences between various $^{13}$C-bearing isotopologues of HC$_{5}$N are evaluated. Overall, the isotopic $^{12}$C/$^{13}$C ratio is estimated to be 49$pm$9. Finally, a comparison of detected molecules in the $lambda$ $sim$1.3 cm range with the dark cloud TMC-1 indicates that silicate-bearing molecules are more predominant in IRC +10216.
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