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ON THE GENERALISATION OF SIDEL’NIKOV’S THEOREM TO $q$-ARY LINEAR CODES

Part of: Theory of error-correcting codes and error-detecting codes Numerical mathematics

Published online by Cambridge University Press:  27 May 2019

YILUN WEI Open the ORCID record for YILUN WEI [Opens in a new window] ,
BO WU Open the ORCID record for BO WU [Opens in a new window]  and
QIJIN WANG Open the ORCID record for QIJIN WANG [Opens in a new window]
YILUN WEI
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China email [email protected]
BO WU
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China email [email protected]
QIJIN WANG*
Affiliation:
Anhui Xinhua University, Hefei, Anhui, 230088, China email [email protected]
*
✉[email protected]
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Abstract

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.

Keywords

q-ary linear codeestimationSidel’nikov’s theorem

MSC classification

Primary: 94B05: Linear codes, general
Secondary: 97N20: Rounding, estimation, theory of errors
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 157 - 162
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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Footnotes

The third author (corresponding author) is supported by Key Project of Natural Science Research of Anhui Higher Education Institutions (K J2018A0589).

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