, , . () . .
, : . n k,
r = n - k. (4.2)
:
- (N0, Nk);
- (χ);
- (dmin);
- (g0);
- .
, n,
N0 = 2n. (4.3)
k
Nk = 2k. (4.4)
, :
N = N0 Nk = 2n - 2k, (4.5)
(4.2) :
N0 /Nk = 2n /2k = 2n-k = 2r, (4.6)
r () .
χ = r/n = (n-k)/n = 1 k/n = 1 log2 Nk / log2 N0, (4.7)
Bk = k/n = 1 χ. (4.8)
, . Bk . ,
B = H∙(k/n), (4.9)
n k .
, , , . , , . , . , .
, , . , , .
, , . . .
(), , . 2 . , xi = 01011 xj = 10010 d(xi, xj), 3,
|
|
xi = 01011 W = 3, xj = 10010 W = 2.
, d(xj, x0) x j (0 = 000) W xi, . . xi 1 .
xi xj = 11001 → d(xj, xj) = 3. (4.10)
2).
. , , (n = k) n, . dmin, , .
, , , dmin = 1. , . , , dmin ≥ 2.
, .
, (1 → 0) (0 → 1). 1→ 0 0 → 1 ( ). , , . (g = 2) (g > 2) 0 ≤ g ≤ n.
, . g0, ,
dmln ≥ g0 + 1. (4.11)
g0 . , g0 :
g0 ≤ dmin 1. (4.12)
gi , , :
dmin ≥ 2 ∙ gu + 1. (4.13)
gu gu + 1 . (4.13) , , g , , . , gu :
|
|
gu ≤ (dmin 1)/2. (4.14)
(4.11) (4.13) , gu, , , g0 = 2 ∙ gu. , (4.11) (4.13) dmin . , dmin = 2 , g0 < n.
g, [8]:
, (4.15)
;
.
, . .
(4.16)
. (4.17)
g, . ,
. (4.18)
(4.18) , P0 n, , .
, , . . (), .
, dmin n k, :
dmin ≤ (n ∙2 ∙ k 1) ∕ (2 ∙ k -1) (4.19)
r ≥ 2 ∙ (dmin - 1) log2 dmin, (4.20)
n ≥ 2 ∙ dmin 1.
(2 k) n dmin:
, (4.21)
n i .
:
. (4.22)
(dmin / n) ≤ 0,3 .
n , :
. (4.23)
, , :
r ≥ log 2 (n + 1 ) dmin = 3;
r ≥ log 2 ( 2 ∙ n) dmin = 4.
dmin = 3 4 .
dmin n k r k dmin.
, , , dmin. dmin . , , .