Nonexistence for extremal Type II $\ZZ_{2k}$-Codes

TL;DR

This paper proves that extremal Type II a0 extbackslash Z_{2k} extbackslash u00a0-codes do not exist for large lengths when k=2,3,4,5,6, clarifying the limitations of such codes.

Contribution

The paper establishes nonexistence results for extremal Type II a0 extbackslash Z_{2k} extbackslash u00a0-codes for large lengths across multiple values of k.

Findings

Extremal Type II a0 extbackslash Z_{2k} extbackslash u00a0-codes do not exist for sufficiently large n.

Nonexistence holds for k=2,3,4,5,6.

Results extend understanding of limitations in code theory.

Abstract

In this paper, we show that an extremal Type II $\ZZ_{2k}$-code of length $n$ dose not exist for all sufficiently large $n$ when $k=2,3,4,5,6$.