TY - JOUR
T1 - Average of complete joint weight enumerators and self-dual codes
AU - Chakraborty, Himadri Shekhar
AU - Miezaki, Tsuyoshi
N1 - Funding Information:
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).
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/6
Y1 - 2021/6
N2 - In this paper, we give a representation of the average of complete joint weight enumerators of two linear codes of length n over Fq and Zk 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 Fq and Zk. Finally, the average of intersection numbers of a pair of Type III (resp. Type IV) codes, and its second moment are found.
AB - In this paper, we give a representation of the average of complete joint weight enumerators of two linear codes of length n over Fq and Zk 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 Fq and Zk. Finally, the average of intersection numbers of a pair of Type III (resp. Type IV) codes, and its second moment are found.
KW - Codes
KW - Equivalence
KW - Weight enumerators
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U2 - 10.1007/s10623-021-00874-8
DO - 10.1007/s10623-021-00874-8
M3 - Article
AN - SCOPUS:85103654194
SN - 0925-1022
VL - 89
SP - 1241
EP - 1254
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 6
ER -