New Upper Bounds for Binary/Ternary Mixed Covering Codes

Reference:

Patric R. J. Östergård and Heikki O. Hämäläinen. New upper bounds for binary/ternary mixed covering codes. Research Report A22, Helsinki University of Technology, Digital Systems Laboratory, Espoo, Finland, March 1993.

Abstract:

A table of upper bounds for K_3,2(n_1,n_2;R), the minimum number of codewords in a covering code with n_1 ternary coordinates, n_2 binary coordinates, and covering radius R, in the range n = n_1+n_2 <= 13, R <= 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) <= 1356.

Keywords:

Code construction, covering code, covering radius, football pool problem, mixed code, simulated annealing

Suggested BibTeX entry:

@techreport{HUT-TCS-A22,
    address = {Espoo, Finland},
    author = {Patric R. J. {\"O}sterg{\aa}rd and Heikki O. H{\"a}m{\"a}l{\"a}inen},
    institution = {Helsinki University of Technology, Digital Systems Laboratory},
    month = {March},
    number = {A22},
    pages = {33},
    title = {New Upper Bounds for Binary/Ternary Mixed Covering Codes},
    type = {Research Report},
    year = {1993},
}