No projective 16-divisible binary linear code of length 131 exists
Sascha Kurz
TL;DR
This paper proves the non-existence of a specific type of binary linear code, leading to improved bounds in network coding and related areas.
Contribution
It establishes the non-existence of a projective 16-divisible binary linear code of length 131, providing new bounds for related coding problems.
Findings
No such code exists for the specified parameters.
Results improve bounds for constant-dimension codes.
Implications for network coding and partial spreads.
Abstract
We show that no projective 16-divisible binary linear code of length 131 exists. This implies several improved upper bounds for constant-dimension codes, used in random linear network coding, and partial spreads.
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