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A346003
Distance 3 lexicode over the alphabet {0,1,2}, with the codewords written in base 10.
5
0, 13, 26, 32, 42, 46, 61, 65, 75, 325, 336, 357, 362, 373, 383, 394, 396, 413, 584, 651, 658, 677, 699, 716, 812, 825, 832, 840, 847, 863, 878, 898, 909, 975, 982, 1001, 1023, 1043, 1048, 1148, 1165, 1170, 1194, 1208, 1223, 1254, 1269, 1330, 1341, 1421, 1452
OFFSET
1,2
COMMENTS
Lexicographically earliest sequence of ternary words such that any two distinct words differ in at least 3 positions.
LINKS
J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235.
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.
MAPLE
(See A346000).
PROG
(Python)
def t(n):
d = []
while n:
d.append(n%3)
n //= 3
return d
def dif(n1, n2):
return sum(d1 != d2 for d1, d2 in zip(n1 + [0] * (len(n2)-len(n1)), n2))
a = [0]
for n in range(2000):
if all(dif(t(n1), t(n)) >= 3 for n1 in a):
a.append(n)
print(a) # Andrey Zabolotskiy, Sep 30 2021
CROSSREFS
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.
Sequence in context: A356064 A180055 A371463 * A164007 A101870 A321714
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Jul 20 2021
EXTENSIONS
Terms a(36) and beyond from Andrey Zabolotskiy, Sep 30 2021
STATUS
approved