The Spectrum of Quantum Caps in PG(4,4)
Daniele Bartoli, Stefano Marcugini, Fernanda Pambianco
TL;DR
This paper determines the possible sizes of quantum caps in PG(4,4), proving the non-existence of certain sizes and implications for related quantum codes, thus completing the spectrum analysis.
Contribution
It establishes the non-existence of quantum caps of sizes 37 and 39 in PG(4,4), completing the spectrum classification and implications for specific quantum codes.
Findings
Quantum caps of sizes 37 and 39 do not exist in PG(4,4)
Non-existence of linear [[37,27,4]] and [[39,29,4]]-codes
Open problem remains for non-linear quantum codes with these parameters
Abstract
We prove the non existence of quantum caps of sizes 37 and 39. This completes the spectrum of quantum caps in PG(4, 4). This also implies the non existence of linear [[37,27,4]] and [[39,29,4]]-codes. The problem of the existence of non linear quantum codes with such parameters remains still open.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · graph theory and CDMA systems