Binomial moments for divisible self-dual codes (Q622780)

Summary: For self-dual codes with all weights divisible by an integer greater than one, the minimum distance is bounded by the Mallows-Sloane upper bounds and by their improvements due to \textit{I. Krasikov, S. Litsyn} [IEEE Trans. Inf. Theory 46, No. 1, 274--278 (2000; Zbl 0997.94037)] and \textit{E. M. Rains} [IEEE Trans. Inf. Theory 49, No. 5, 1261--1274 (2003; Zbl 1063.94123)]. We obtain the improved upper bounds from short relations with constant coefficients on suitable binomial moments of the codes. In this approach, the Mallows-Sloane bounds are analogues of the Singleton bound and the improved bounds are analogues of the Plotkin bound.