No abstract

In this note, we describe the parity of the coefficients of the McKay-Thompson series of Mathieu moonshine. As an application, we prove a conjecture of Cheng, Duncan and Harvey stated in connection with umbral moonshine for the case of Mathieu moonshine. ∞ n=−∞ q 1 2 (n+ 1 2 ) 2 e 2πi(n+ 1 2 )(z+ 1 2 ) .

Let D be the support design of the minimum weight of an extremal binary doubly even self-dual [24m,12m,4m+4] code. In this note, we consider the case when D becomes a t-design with t \geq 6.Comment: 8 page

For lengths 8, 16 and 24, it is known that there is an extremal Type II Z 2k -code for every positive integer k. In this paper, we show that there is an extremal Type II Z 2k -code of lengths 32, 40, 48, 56 and 64 for every positive integer k. For length 72, it is also shown that there is an extremal Type II Z 4k -code for every positive integer k with k ≥ 2.

No abstract