Second support weights for binary self-dual codes

Abstract

In this work, we investigate the second generalized Hamming weights for binary doubly-even self-dual codes from the point of view of corresponding t-designs by the Assmus-Mattson theorem. In particular, for extremal doubly-even self-dual codes, we shall give a bound on the weights and determine the weights by using the block intersection numbers of corresponding t-designs. Moreover we study the support weight enumerators for binary doubly-even self-dual codes and determine the second support weight enumerators for binary extremal doubly-even self-dual codes of length 56 and 96. © Springer-Verlag Berlin Heidelberg 2006.