Graphs associated with codes of covering radius 1 and minimum distance 2 (Q1010788)

Summary: The search for codes of covering radius 1 led \textit{P. R. J. Östergård, J. Quistorff} and \textit{A. Wassermann} [Des. Codes Cryptography 35, No. 2, 241--250 (2005; Zbl 1081.94041)] to the OQW method of associating a unique graph to each code. We present results on the structure and existence of OQW-associated graphs. These are used to find an upper bound on the size of a ball of radius 1 around a code of length 3 and minimum distance 2. OQW-associated graphs and non-extendable partial Latin squares are used to catalogue codes of length 3 over 4 symbols with covering radius 1 and minimum distance 2.