On triply even binary codes

Abstract

A triply even code is a binary linear code in which the weight of every codeword is divisible by 8. We show how two doubly even codes of lengths m1 and m2 can be combined to make a triply even code of length m1+m2, and then prove that every maximal triply even code of length 48 can be obtained by combining two doubly even codes of length 24 in a certain way. Using this result, we show that there are exactly ten maximal triply even codes of length 48 up to equivalence. © 2012 London Mathematical Society.