On the Minimal Weight of Some Singly-Even Codes
by
Vassil Yorgov
Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931

Let t be an even positive integer such that \frac(5t)!t!(4t)! be odd. It is shown that if a singly-even self-dual [24t+8, 12t+4] code with a weight 4 vector in its shadow exists then d <= 4t+2 . This is an improvement of the Rains bound, d <= 4t+4 , in this special case. As a concequence it is obtained nonexistence of a [56, 28, 12] singly-even self-dual code with 4862 weight 12 vectors. This was an open question raised by Conway and Sloane in their joint paper in 1990.

Date received: November 5, 1998