

A139767


Let e = 2n+1; consider the cyclotomic cosets C_i of 2 mod e; a(n) = maximal value of minimal number of copies of C_1 needed to add together to get any coset C_i.


3



1, 1, 2, 2, 1, 1, 3, 2, 1, 3, 2, 2, 2, 1, 4, 3, 3, 1, 2, 2, 2, 4, 2, 3, 3, 1, 2, 3, 1, 1, 5, 3, 1, 3, 2, 3, 4, 3, 2, 2, 1, 4, 2, 3, 3, 5, 2, 2, 3, 1, 2, 4, 1, 2, 2, 2, 3, 3, 3, 2, 3, 2, 6, 4, 1, 3, 4, 2, 1, 3, 2, 3, 3, 1, 3, 4, 5, 2, 2, 3, 1, 4, 2, 2, 3, 1, 3, 3, 1, 1, 2, 3, 2, 6, 2, 2, 4, 1, 2
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OFFSET

1,3


COMMENTS

C_i = {i, 2i, 4i, ... } reduced mod e.


REFERENCES

F. J. MacWilliams and N. J. A. Sloane, The Theory of ErrorCorrecting Codes, NorthHolland/Elsevier, 1977; see p. 104 for definition of cyclotomic coset.


LINKS



EXAMPLE

Let n=7, e=15: the cyclotomic cosets of 2 mod 15 are
C_0 := {0}
C_1 := {1 2 4 8}
C_3 := {3 6 12 9}
C_5 := {5 10}
C_7 := {1 2 4 8} == {14 13 11 7}
and to get an element of C_7 we must add three elements of C_1;
this is the worst case, so a(7) = 3.


CROSSREFS

Records occur when e is of the form 2^j  1. Sequence is 1 iff e is in A001122. A140364 lists e such that the sequence is 2.


KEYWORD

nonn


AUTHOR



STATUS

approved



