Abstract
In this paper, we give a representation of the average of complete joint weight enumerators of two linear codes of length n over \(\mathbb {F}_q\) and \(\mathbb {Z}_k\) in terms of the compositions of n and their distributions in the codes. We also obtain a generalization of the representation for the average of g-fold complete joint weight enumerators of codes over \(\mathbb {F}_q\) and \(\mathbb {Z}_{k}\). Finally, the average of intersection numbers of a pair of Type \(\mathrm{{III}}\) (resp. Type \(\mathrm{{IV}}\)) codes, and its second moment are found.
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Acknowledgements
The authors thank Manabu Oura for helpful discussions. The authors would also like to thank the anonymous reviewers for their beneficial comments on an earlier version of the manuscript. The second named author is supported by JSPS KAKENHI (18K03217).
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Communicated by J. Bierbrauer.
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Chakraborty, H.S., Miezaki, T. Average of complete joint weight enumerators and self-dual codes. Des. Codes Cryptogr. 89, 1241–1254 (2021). https://doi.org/10.1007/s10623-021-00874-8
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DOI: https://doi.org/10.1007/s10623-021-00874-8