Classification of small binary/ternary one-error-correcting codes

This is the electronic site for the paper "P. R. J. Östergård, Classification of small binary/ternary one-error-correcting codes, Discrete Mathematics 223 (2000), 253-262".

All but five of the optimal codes reported in the paper are listed in its Appendix. Here, we make all codes found in the study available electronically, including all intermediate codes needed in the optimality proofs. The parameters of the codes are (n2,n3,d)M, where n2 is the number of binary coordinates, n3 is the number of ternary coordinates, M is the number of codewords, and d is a lower bound on the minimum Hamming distance.

In the files, the codes are given in the following form. The files contain one integer per line. The first line gives the number of codes. The second line gives n2 and the third line n3. After this, all codes come consecutively with the following format: an initial line tells the number of codewords (M), and the following M lines give these words in encoded form.

Mixed radix encoding is used: A word (c(1),c(2),...,c(n)) is transformed into c(1)*m(1)+c(2)*m(2)+...+c(n)*m(n), where m(1) = 1 and m(i+1) = d(i)*m(i), where d(i) is the cardinality of coordinate i. The ternary coordinates are in the least significant positions.

(2,1,3)1: 1 code
(2,1,3)2: 1 code
(3,1,3)2: 3 codes
(3,1,3)3: 1 code
(4,1,3)4: 6 codes
(4,1,3)5: 1 code
(4,1,3)6: 1 code
(5,1,3)7: 47 codes
(5,1,3)8: 18 codes
(6,1,3)13: 15714 codes
(6,1,3)14: 2223 codes
(6,1,3)15: 272 codes
(6,1,3)16: 46 codes
(7,1,3)26: 33097 codes
(1,2,3)2: 1 code
(2,2,3)3: 2 codes
(2,2,3)4: 1 code
(3,2,3)5: 14 codes
(3,2,3)6: 8 codes
(4,2,3)10: 401 codes
(4,2,3)11: 21 codes
(4,2,3)12: 3 codes
(5,2,3)19: 40955 codes
(5,2,3)20: 1338 codes
(5,2,3)21: 43 codes
(5,2,3)22: 3 codes
(6,2,3)37: 3062 codes
(6,2,3)38: 11 codes
(0,3,3)2: 1 code
(0,3,3)3: 1 code
(1,3,3)4: 3 codes
(1,3,3)5: 1 code
(1,3,3)6: 1 code
(2,3,3)7: 66 codes
(2,3,3)8: 14 codes
(2,3,3)9: 3 codes
(3,3,3)14: 2045 codes
(3,3,3)15: 126 codes
(3,3,3)16: 26 codes
(3,3,3)17: 4 codes
(3,3,3)18: 2 codes
(4,3,3)27: 4109 codes
(4,3,3)28: 51 codes
(5,3,3)54: 6 codes
(6,3,3)108: 4 codes
(0,4,3)5: 5 codes
(0,4,3)6: 4 codes
(0,4,3)7: 1 code
(0,4,3)8: 1 code
(0,4,3)9: 1 code
(1,4,3)10: 74 codes
(1,4,3)11: 2 codes
(1,4,3)12: 1 code
(2,4,3)19: 25703 codes
(2,4,3)20: 668 codes
(2,4,3)21: 23 codes
(2,4,3)22: 2 codes
(3,4,3)37: 21003 codes
(3,4,3)38: 1658 codes
(3,4,3)39: 147 codes
(3,4,3)40: 22 codes
(3,4,3)41: 2 codes
(3,4,3)42: 1 code
(0,5,3)13: 1533 codes
(0,5,3)14: 78 codes
(0,5,3)15: 10 codes
(0,5,3)16: 3 codes
(0,5,3)17: 1 code
(0,5,3)18: 1 code
(1,5,3)28: 41964 codes
(1,5,3)29: 4343 codes
(1,5,3)30: 474 codes
(1,5,3)31: 53 codes
(1,5,3)32: 8 codes
(1,5,3)33: 2 codes
(0,6,3)38: 1 code


Last update: April 16, 2019 by Patric Östergård.