Note on the residue codes of self-dual ${\mathbb{Z}}_4$-codes having large minimum Lee weights

Abstract

It is shown that the 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 code for 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 the above characterization. These codes are Type I ${\mathbb{Z}}_4$-codes having the largest minimum Lee weight and the largest Euclidean 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.

18 pages

References in corpus (1)

• The Z_4-Linearity of Kerdock, Preparata, Goethals and Related Codes