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An explicit representation and enumeration for self-dual cyclic codes over 𝔽2m + u𝔽2m of length 2s

Authors: 

Yuan Cao, Yonglin Cao, Hai Q. Dinh, Somphong Jitman

Source title: 
Discrete Mathematics, 342(7): 2077-2091, 2019 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

Let 22_QuangHai.png be a finite field of cardinality  2m and s a positive integer. Using properties for Kronecker product of matrices and calculation for linear equations over 22_QuangHai.png, an efficient method for the construction of all distinct self-dual cyclic codes with length  over the finite chain ring  31_QuangHai.png is provided. On that basis, an explicit representation for every self-dual cyclic code of length 2s over 30_QuangHai.png and an exact formula to count the number of all these self-dual cyclic codes are given.