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A128037 Maximal possible number of vectors in {0,1,2,3}^n such that the Hamming distance between every two is odd. 1

%I #13 Jan 11 2020 19:51:58

%S 4,4,6,9,12,12,14

%N Maximal possible number of vectors in {0,1,2,3}^n such that the Hamming distance between every two is odd.

%H N. Alon and E. Lubetzky, <a href="https://www.researchgate.net/publication/225118372_Codes_And_Xor_Graph_Products">Codes and XOR graph products</a>, Combinatorica, 27 (No. 1, 2007), 13-33. [See g_4(n).]

%e From _Bert Dobbelaere_, Jan 07 2019: (Start)

%e Lexicographically earliest maximal sets:

%e a(1) = 4 {0, 1, 2, 3}

%e a(2) = 4 {00, 01, 02, 03}

%e a(3) = 6 {000, 001, 002, 113, 123, 133}

%e a(4) = 9 {0000, 0001, 0002, 0113, 0123, 0133, 1203, 2203, 3203}

%e a(5) = 12 {00000, 00001, 00002, 00113, 00123, 00133, 01203, 02203, 03203, 10303, 20303, 30303}

%e a(6) = 12 {000000, 000001, 000002, 000113, 000123, 000133, 001203, 002203, 003203, 010303, 020303, 030303}

%e a(7) = 14 {0000000, 0000001, 0000002, 0000113, 0000123, 0000133, 0001203, 0002203, 0003203, 0010303, 0020303, 1130303, 1230303, 1330303}

%e (End)

%Y Cf. A128036.

%K nonn,nice,more

%O 1,1

%A Alon Noga (nogaa(AT)post.tau.ac.il) and Eyal Lubetzky (lubetzky(AT)post.tau.ac.il), May 03 2007

%E a(6)-a(7) from _Bert Dobbelaere_, Jan 07 2019

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Last modified July 7 17:27 EDT 2024. Contains 374107 sequences. (Running on oeis4.)