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Published online by Cambridge University Press: 27 May 2019
We generalise Sidel’nikov’s theorem from binary codes to $q$-ary codes for
$q>2$. Denoting by
$A(z)$ the cumulative distribution function attached to the weight distribution of the code and by
$\unicode[STIX]{x1D6F7}(z)$ the standard normal distribution function, we show that
$|A(z)-\unicode[STIX]{x1D6F7}(z)|$ is bounded above by a term which tends to
$0$ when the code length tends to infinity.
The third author (corresponding author) is supported by Key Project of Natural Science Research of Anhui Higher Education Institutions (K J2018A0589).