There is no [21, 5, 14] code over F5
Makoto Araya, Masaaki Harada
TL;DR
This paper proves that a specific type of error-correcting code, the [21, 5, 14] code, cannot exist over the finite field F5, clarifying limitations in coding theory.
Contribution
The paper establishes a non-existence result for the [21, 5, 14] code over F5, providing a definitive answer to an open question in coding theory.
Findings
No [21, 5, 14] code exists over F5
Clarifies limitations in code constructions over F5
Contributes to classification of codes over finite fields
Abstract
In this note, we demonstrate that there is no [21, 5, 14] code over F5.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Error Correcting Code Techniques