The 95256-cap in PG(12; 4) is complete
D. Bartoli, S. Marcugini, A. Milani, F. Pambianco
TL;DR
This paper presents an algorithm to test the completeness of caps in projective geometries over finite fields, successfully verifying the completeness of a large cap in PG(12; 4) recently discovered.
Contribution
It introduces a new algorithm for testing cap completeness in PG(r; q) for even q, and applies it to confirm the completeness of a specific large cap.
Findings
The 95256-cap in PG(12; 4) is complete.
The algorithm effectively verifies cap completeness in finite projective spaces.
The method can be applied to other caps in similar geometries.
Abstract
We describe an algorithm for testing the completeness of caps in PG(r; q), q even. It allowed us to check that the 95256-cap in PG(12; 4) recently found by Fu el al. (see [14]) is complete.
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Taxonomy
TopicsCoding theory and cryptography · Cryptography and Residue Arithmetic · graph theory and CDMA systems