1 results
ON THE GENERALISATION OF SIDEL’NIKOV’S THEOREM TO
$q$-ARY LINEAR CODES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 101 / Issue 1 / February 2020
- Published online by Cambridge University Press:
- 27 May 2019, pp. 157-162
- Print publication:
- February 2020
-
- Article
- Export citation
-
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.
