Logarithms, Syndrome Functions, and the Information Rates of Greedy Loop Transversal Codes

The paper studies linear block codes and syndrome functions built by the greedy loop transversal algorithm. The syndrome functions in the binary white-noise case are generalizations of the logarithm, exhibiting curious fractal properties. The codes in the binary white-noise case coincide with lexicodes; their dimensions are listed for channel lengths up to sixty, and up to three hundred for double errors. In the ternary double-error case, record-breaking codes of lengths \(43\) to \(68\) are constructed.