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List of the 14 blocks in the Reed-Muller version of the Steiner System S(3,4,8) written as decimal numbers.
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%I #22 Oct 18 2022 01:17:37

%S 15,51,60,85,90,102,105,150,153,165,170,195,204,240

%N List of the 14 blocks in the Reed-Muller version of the Steiner System S(3,4,8) written as decimal numbers.

%C This is a constant weight binary code of length 8, distance 4 and weight 4.

%C It is also a lexicographic code.

%C It is also the set of weight 4 words in the extended Hamming code of length 8.

%H A. E. Brouwer, J. B. Shearer, N. J. A. Sloane and W. D. Smith, <a href="http://dx.doi.org/10.1109/18.59932">New table of constant weight codes</a>, IEEE Trans. Info. Theory 36 (1990), 1334-1380.

%H J. H. Conway and N. J. A. Sloane, <a href="http://dx.doi.org/10.1109/TIT.1986.1057187">Lexicographic codes: error-correcting codes from game theory</a>, IEEE Transactions on Information Theory, 32:337-348, 1986.

%e The blocks are:

%e 00001111

%e 00110011

%e 00111100

%e 01010101

%e 01011010

%e 01100110

%e 01101001

%e 10010110

%e 10011001

%e 10100101

%e 10101010

%e 11000011

%e 11001100

%e 11110000

%Y A subsequence of A075928.

%K fini,full,nonn,base

%O 1,1

%A _N. J. A. Sloane_, Sep 04 2011