The nonexistence of an additive quaternary [15,5,9]-code
Daniele Bartoli, Juergen Bierbrauer, Giorgio Faina, Stefano Marcugini,, Fernanda Pambianco
TL;DR
This paper proves that an additive quaternary [15,5,9]-code does not exist, establishing the maximum dimension for such codes as 4.5, which impacts coding theory limitations.
Contribution
It provides a proof of nonexistence for a specific class of additive quaternary codes, clarifying the boundaries of code parameters.
Findings
No additive [15,5,9]_4-code exists.
Maximum dimension for such codes is 4.5.
Implications for coding theory limitations.
Abstract
We show that no additive [15,5,9]_4-code exists. As a consequence the largest dimension k such that an additive quaternary [15,k,9]_4-code exists is k=4.5.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Error Correcting Code Techniques