The support designs of the triply even codes of length 48

Tsuyoshi Miezaki, Hiroyuki Nakasora

Published 2018-05-25Version 1

A triply even code is a binary linear code in which the weight of every codeword is divisible by 8. The triply even codes of length 48 have been classified by Betsumiya and Munemasa. Herein we study the support designs of triply even codes of length 48 and present the complete list of triply even codes of length 48 with the support 1-designs obtained from the Assmus-Mattson theorem. Moreover, we show that some of such codes have the support 2-designs. This is the first example of a code having the support t-designs for all weights obtained from the Assmus-Mattson theorem and has the support t'-designs for some weight with some t'>t.