The lengths of projective triply-even binary codes

Abstract

It is shown that there does not exist a binary projective triply-even code of length $59$. This settles the last open length for projective triply-even binary codes. Therefore, projective triply-even binary codes exist precisely for lengths $15$, $16$, $30$, $31$, $32$, $45$--$51$, and $\ge 60$.

12 pages, 4 tables

Cited by in corpus (2)

• Computer classification of linear codes
• No projective 16-divisible binary linear code of length 131 exists