... a 10 -bit Gray code
with minimum run length 8. This is the Gray code used in the Codacon device [4]. The
construction in Section 3 and those given in [1, 2] can only produce 10 -bit codes with
minimum ... require
specialized Gray codes with properties not possessed by the RGC. We refer to Savage [6]
for more information on such variations. This paper is concerned with Gra...
... [7] of a code. Gray codes which
are uniform with respect to the former measure are referred to as balanced Gray codes.
To make this notion precise, associate with an n -bit cyclic Gray code L
n
= ... an n -bit Gray code in which every bit position changes a
n
or
a
n
+2 times.
Proof. For n =1, 2, 3, the BRGC scheme gives a Gray code satisfying this property. In
Figure 2 w...
... on Codes with
Covering Radius 1 and Minimum Distance 2, Des. Codes Cryptogr., 35 (2005), 241-
250.
[7] Quistorff, J.: On Full Partial Quasigroups of Finite Order and Local Cardinal Maxi-
mum Codes, ... 14 (2007), #R51 5
code C ⊂ Q
n
with minimum distance d, and K
q
(n, R), the minimal cardinality of a code
C ⊂ Q
n
with covering radius R, see [2].
q-ary codes with covering radius...
... integers of O(N) bits or the division of an integer of
O(N) bits by a “small” integer, of O(log(N)) bits.
Proposition 10. The N first coefficients counting combinatorial d-polytopes with d +3
vertices ... Property P2 (or S2), we introduce the three subalphabets
B =
i
j
with i>0,j >0
, C =
i
0
with i>0
, D =
0
j
with j>0
,
which partition the alphabet A. P...
... b]tobe(L, R, O, Z), with O the number of 1’s in
the interval; Z the number of 0’s in the interval; L the minimal nonnegative number
with a + L a1;Rthe minimal nonnegative number with b − R a 1 – ... models also satisfy Σ ∪ (∀x)(¬U(x)), namely
those with arbitrarily many copies of of chains of 0’s, ordered like the integers (called
“Z-chains”), with an infinite decreasing chain of 0’s...