Average of complete joint weight enumerators and self-dual codes

2020/06/23 by Chakraborty, Himadri Shekhar, Miezaki, Tsuyoshi
#11F11 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Primary: 11T71 #Secondary: 94B05

paper · doi:10.48550/arxiv.2006.12781

Abstract

In this paper, we give a representation of the average of complete joint weight enumerators of two linear codes of length n over \mathbbF_q and 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 \mathbbF_q and ℤ_k. Finally, the average of intersection numbers of a pair of Type III (resp. Type IV) codes, and its second moment are found.

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