Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 2, pp. 445-449 (2002)

Classifying Optimal Ternary Codes of Length 5 and Covering Radius 1

Patric R. J. Östergard, William D. Weakley

Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, 02015 HUT, Finland e-mail: patric.ostergard@hut.fi; Department of Mathematical Sciences Indiana University - Purdue University Fort Wayne Fort Wayne, Indiana 46805, e-mail: weakley@ipfw.edu

Abstract: It is well known that optimal ternary codes of length 5 and covering radius 1 have 27 codewords. The structure of such optimal codes has been studied, but a classification of these is still lacking. In this work, a complete classification is carried out by constructing codes coordinate by coordinate in a backtrack search. Linear inequalities and equivalence checking are used to prune the search. In total there are 17 optimal codes.

Keywords: backtrack search, code equivalence, covering code, football pool problem, nonlinear code, ternary code

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