A128036 Maximal possible number of vectors in {0,1,2}^n such that the Hamming distance between every two is odd.

3, 3, 4, 9, 9, 11, 13, 17, 19

Offset

1,1

Comments

The sequence f_3(n) (the analog for even Hamming distances) is probably 2^(n-1) for odd values of n and that value plus 1 for even n.

Links

Table of n, a(n) for n=1..9.

N. Alon and E. Lubetzky, Codes and XOR graph products, Combinatorica, 27 (No. 1, 2007), 13-33. [See g_3(n).]

Fausto A. C. Cariboni, A maximal set for a(9) = 19, Nov 17 2019.

Rahul Sarkar, Ewout van den Berg, On sets of commuting and anticommuting Paulis, arXiv:1909.08123 [quant-ph], 2019.

Example

Lexicographically earliest maximal sets:
a(1) = 3 {0, 1, 2}
a(2) = 3 {00, 01, 02}
a(3) = 4 {000, 001, 112, 122}
a(4) = 9 {0000, 0111, 0222, 1012, 1120, 1201, 2021, 2102, 2210}
a(5) = 9 {00000, 00111, 00222, 01012, 01120, 01201, 02021, 02102, 02210}
a(6) = 11 {000000, 000111, 000222, 001012, 010120, 111201, 212012, 221120, 222021, 222102, 222210}
a(7) = 13 {0000000, 0000111, 0000222, 0001012, 0001120, 0001201, 0002021, 0112102, 0222210, 1012210, 1202102, 2022102, 2102210}
a(8) = 17 {00000000, 00000111, 00000222, 00001012, 00010120, 01102012, 02220120, 10120120, 11211201, 12002012, 20202012, 21020120, 22112012, 22121120, 22122021, 22122102, 22122210}

Crossrefs

Cf. A128037.

Sequence in context: A016605 A185395 A060372 * A332311 A332340 A045794

Adjacent sequences: A128033 A128034 A128035 * A128037 A128038 A128039

Keyword

nonn,nice,more

Author

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

Extensions

a(7)-a(8) from Bert Dobbelaere, Dec 26 2018

a(9) from Fausto A. C. Cariboni, Nov 17 2019

Status

approved