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Distance 3 lexicode over the alphabet {0,1,2}, with the codewords written in base 10.
5

%I #16 Sep 30 2021 12:13:00

%S 0,13,26,32,42,46,61,65,75,325,336,357,362,373,383,394,396,413,584,

%T 651,658,677,699,716,812,825,832,840,847,863,878,898,909,975,982,1001,

%U 1023,1043,1048,1148,1165,1170,1194,1208,1223,1254,1269,1330,1341,1421,1452

%N Distance 3 lexicode over the alphabet {0,1,2}, with the codewords written in base 10.

%C Lexicographically earliest sequence of ternary words such that any two distinct words differ in at least 3 positions.

%H Andrey Zabolotskiy, <a href="/A346003/b346003.txt">Table of n, a(n) for n = 1..6000</a>

%H J. H. Conway, <a href="https://doi.org/10.1016/0012-365X(90)90008-6">Integral lexicographic codes</a>, Discrete Mathematics 83.2-3 (1990): 219-235.

%H J. H. Conway and N. J. A. Sloane, <a href="https://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.

%p (See A346000).

%o (Python)

%o def t(n):

%o d = []

%o while n:

%o d.append(n%3)

%o n //= 3

%o return d

%o def dif(n1, n2):

%o return sum(d1 != d2 for d1, d2 in zip(n1 + [0] * (len(n2)-len(n1)), n2))

%o a = [0]

%o for n in range(2000):

%o if all(dif(t(n1), t(n)) >= 3 for n1 in a):

%o a.append(n)

%o print(a) # _Andrey Zabolotskiy_, Sep 30 2021

%Y Lexicodes of minimal distance 1,2,3,... over alphabets of size 2: A001477, A001969, A075926, A075928, A075931, A075934, ...; size 3: A001477, A346002, A346003; size 10: A001477, A343444, A333568, A346000, A346001.

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, Jul 20 2021

%E Terms a(36) and beyond from _Andrey Zabolotskiy_, Sep 30 2021