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The lengths of projective triply-even binary codes

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arxiv 1812.05957 v1 pith:UMKDLHVF submitted 2018-12-14 math.CO cs.ITmath.IT

Thomas Honold , Michael Kiermaier , Sascha Kurz , Alfred Wassermann This is my paper · ORCID
classification math.COcs.ITmath.IT
keywords binaryprojectivetriply-evencodesexistlengthlengthscode
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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 $\ge 60$.

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