Note on the residue codes of self-dual $\mathbb{Z}_4$-codes having large minimum Lee weights
Masaaki Harada · Advances in Mathematics of Communications · 2016
It is shown thatthe residue code of a self-dual $\mathbb{Z}_4$-code of length $24k$(resp. $24k+8$)and minimum Lee weight $8k+4 \text{ or }8k+2$(resp. $8k+8 \text{ or }8k+6$)is a binary extremal doubly even self-dual codefor every positive integer $k$.A number of new self-dual $\mathbb{Z}_4$-codes of length $24$and minimum Lee weight $10$ are constructed using theabove characterization.These codes are Type I $\mathbb{Z}_4$-codeshaving the largest minimum Lee weight and the largestEuclidean weight among all Type I $\mathbb{Z}_4$-codes of that length.In addition, new extremal Type II $\mathbb{Z}_4$-codes of length$56$ are found.