New Upper Bounds for Binary/Ternary Mixed Covering Codes

摘要

A table of upper bounds for K(3,2)(n(1),n2;R), the minimum number of codewords ina covering code with n(1) ternary coordinates, n(2) binary coordinates, and covering radius R, in the range n=n(1)+n(2) = or < 13, R = or < 3, is presented. Explicit constructions of codes are given to prove the new bounds and verify old bounds. These binary/ternary covering codes can be used as systems for the football pool game. The results include a new upper bound for the football pool problem for 9 matches, showing that K(3)(9,1) = or < 1356.