Optimal binary one-error-correcting codes of length 10 have 72 codewords

This is the electronic site for the paper "P. R. J. Östergård, T. Baicheva, and E. Kolev, Optimal binary one-error-correcting codes of length 10 have 72 codewords, IEEE Transactions on Information Theory 45 (1999), 1229-1231".

The codes reported in the paper are not explicitly given, but are electronically available here. The parameters of the codes are (n,M,d), where n is the length of the code, M is the number of codeword, 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 the length of the code (n). 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 decimal form.

(4,2,3): 2 codes
(5,3,3): 1 code
(5,4,3): 1 code
(6,5,3): 4 codes
(6,6,3): 4 codes
(6,7,3): 1 code
(6,8,3): 1 code
(7,9,3): 191 codes
(7,10,3): 90 codes
(7,11,3): 27 codes
(7,12,3): 16 codes
(7,13,3): 4 codes
(7,14,3): 3 codes
(7,15,3): 1 code
(7,16,3): 1 code
(8,18,3): 17547 codes
(8,19,3): 216 codes
(8,20,3): 5 codes
(9,36,3): 19502 codes
(9,37,3): 732 codes
(9,38,3): 58 codes
(9,39,3): 3 codes
(9,40,3): 1 code
(10,72,3): 562 codes
(11,144,3): 7398 codes
(5,2,4): 2 codes
(6,4,4): 1 code
(7,8,4): 1 code
(8,16,4): 1 code
(9,20,4): 3 codes
(10,40,4): 1 code
(11,72,4): 96 codes
(12,144,4): 1041 codes


Latest update: July 2, 2019.