On the existence of extremal Type II ℤ_{2𝕜}-codes
Masaaki Harada, Tsuyoshi Miezaki · Mathematics of Computation · 2013
For lengths 8 8 , 16 16 , and 24 24 , it is known that there is an extremal Type II Z 2 k \mathbb {Z}_{2k} -code for every positive integer k k . In this paper, we show that there is an extremal Type II Z 2 k \mathbb {Z}_{2k} -code of lengths 32 , 40 , 48 , 56 32,40,48,56 , and 64 64 for every positive integer k k . For length 72 72 , it is also shown that there is an extremal Type II Z 4 k \mathbb {Z}_{4k} -code for every positive integer k k with k ≥ 2 k \ge 2 .