Linear and non-linear loop-transversal codes in error-correction and graph domination
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 295-309
Published online January 7, 2020
Printed March 31, 2020
Mehmet Da\v{g}l{\i}, Bokhee Im, Jonathan D. H. Smith
Amasya University; Chonnam National University; Iowa State University
Abstract : Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.
Keywords : Loop transversal code, nonlinear code, quasigroup, loop, circulant graph, efficient domination
MSC numbers : 94B60, 20N05, 05C69
Supported by : The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2017R1D1A3B05029924).
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