Construction of non-free extremal Type II codes over Z_{2^m}

Extremal Type II ℤ₂^m-codes are a class of self-dual ℤ₂^m -codes with Euclidean weights divisible by 2m+1 and the largest possible minimum Euclidean weight for a given length.

We introduce a doubling method for constructing a Type II ℤ₂^m -code of length n from a known Type II ℤ₂^m -code of length n. Based on this method, we develop an algorithm to construct non-free extremal Type II ℤ₂^m -codes starting from a free extremal Type II ℤ₂^m -code with an extremal ℤ₂^m-1 -residue code and length 24, 32 or 40.

We obtain at least 10 new extremal Type II ℤ₈ -codes of length 32 and at least 11 new extremal Type II ℤ₁₆ -codes of length 32.

Joint work with Sanja Rukavina.