8th Croatian Mathematical Congress

New extremal Type II $\mathbb{Z}_{4}$-codes via doubling method

5 Jul 2024, 10:50

20m

D3 (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

Talk CDM: Combinatorics and Discrete Mathematics Combinatorics and Discrete Mathematics

Speaker

Sara Ban (Faculty of Mathematics, University of Rijeka)

Description

The doubling method is a method for constructing Type II $\mathbb{Z}_4$-codes from a given Type II $\mathbb{Z}_4$-code.

Extremal Type II $\mathbb{Z}_4$-codes are a class of self-dual $\mathbb{Z}_4$-codes with Euclidean weights divisible by eight and the largest possible minimum Euclidean weight for a given length. A small number of such codes is known for lengths greater than or equal to $48.$

The subject of this talk is a construction of new extremal Type II $\mathbb{Z}_4$-codes of length $64$ by the doubling method.

We develop a method to construct new extremal Type II $\mathbb{Z}_4$-codes starting from an extremal Type II $\mathbb{Z}_4$-code of type $4^k$ with an extremal residue code and length $48, 56$ or $64$.
Using this method, we construct three new extremal Type II $\mathbb{Z}_4$-codes of length $64$ and type $4^{31}2^2$. Extremal Type II $\mathbb{Z}_4$-codes of length $64$ of this type were not known before.