A194851 List of the 14 blocks in the Reed-Muller version of the Steiner System S(3,4,8) written as decimal numbers.

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

Offset: 1

Author

N. J. A. Sloane, Sep 04 2011

Keywords

• fini
• full
• nonn
• base

Comments

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

It is also a lexicographic code.

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

Examples

			The blocks are:
00001111
00110011
00111100
01010101
01011010
01100110
01101001
10010110
10011001
10100101
10101010
11000011
11001100
11110000
		

Links

• A. E. Brouwer, J. B. Shearer, N. J. A. Sloane and W. D. Smith, New table of constant weight codes, IEEE Trans. Info. Theory 36 (1990), 1334-1380.
• J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Transactions on Information Theory, 32:337-348, 1986.

Crossrefs

A subsequence of A075928.