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Logarithms, syndrome functions, and the information rates of greedy loop transversal codes. (English) Zbl 0868.94044

Summary: 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, with curious fractal properties. The codes in the binary white-noise case coincide with lexicodes: their dimensions are listed for channel lengths up to the sixties, and up to the three hundreds for double errors. In the ternary double-error case, record-breaking codes of lengths 43 to 68 are constructed.

MSC:

94B05 Linear codes (general theory)
20N05 Loops, quasigroups
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