КОДЫ, КОМПОЗИЦИИ И РЕШЕТКИ

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  • 2008 1(1)

    519.1

    ,

    ..

    , .

    E-mail: maglinetc@mail.ru

    , . -

    , -

    -. . -

    .

    : , , , , s-, -

    - . - , , s- [1 7].

    , L = < M; +, > L = < M; , >, M . .

    . n d (n, d), (n, , d)-, , . [8]. [9]: R = k/n , R , d : d, ( k ). .

    A(m, l, d), A(m, l, d) v l(v) = n m d; .

    1. L-

    ( -). A = {a0, , am} W v l(v) = n A; (, -) A. u = x1 xn u = n-, xi A, i = 1, , n. (-) (). L-, -, 1.

    1. W v l(v) = n, , A = {a0, , am} m+1 W, A, LA = W, , - ci j = (a0, , a0, aj , a0, , a0), aj j- . :

    1) LA , nm+1, - i l(i) n: LA = 1ni, - , - i, ;

    2) n i n = l(v) v ( ), l(i) i m = l(i), m+1=A A, l(LA) = l(1ni) = 1n l(i) = nm;

    3) - nm+1, cik cjt = i j, v - v = ckm -, : v ckm ckm ckm;

    4) - - LA - LA, - m -, LA , -, .

    , L, L = 1ni m, , - , - LA n A = {0, 1, , m}.

    LA L(m, n), m+1=A L(n) m, cik k, ci -.

  • 16 ..

    - r: r(v, u) = r(vu) r(vu), v, uLA, r(x) LA ( ,r(x) x LA), H- : w(x) x, (x, y) = w(x y) , x y; , LA n, n -, = n .

    1. L(n) Sn -, n , Sn / - S(A) , / L(n), - , .

    LA A - r H- . , , A.

    1 : , , .. , . 1 3, . 2 [1] - Sn.

    L- , - , , , - W A , - , LA. -, , .

    . 1. 3 A = {0, 1, 2}. -

    ( 6, 4, 2, 0) d0 = 2

    , A = {0, 1} , - n- , L(m, n) n- , Ci , . [1]. - c 23 3 A = {0, 1} - 000 -111 . . 1, ( ) - A1 A2 A1 A2 n A1 n + k A2, k 0, -, k = 0 - n A1 = {1, , m} {0, 1,, m} = A2 - 11 - mm; , I = [11, mm], L(n, m) A1 = {1, , m}: I L(n, m).

  • , 17

    . 1 - 0 nm = 9 : 1) ai m ai = j, j

    j-, 0 j nm ( 3 j nm); 2) ai = j n;- 3, i ,

    i = 1, 2, 3;- ( 3) -

    ;- , - -

    piki, , . 1, ki ;

    - , mn = 33 = 27., L(m, n) (

    n m , , -, ).

    -, - L(m, n), , , . -

    1. , .. , L(n), , , .

    . . , - L(m, n) -. -- ci, cj L(n), r(ci, cj) d0 - . vk = ci, ut = vk, ws = ut .. -. - v = ci u = cj r(v, u) d0, - 1.

    1. v = ci, u = cj r(ci, cj) d0 ci, cj. r(v, u) r(ci, cj) d0. 1 - d0 2,

    v u r(v, u) d0. , L(2, 3) 200, 020, 002(. . 1) ci, ci .., - 000, 200, 020, 002, 220, 202, 022, 222, v u r(v, u) d0 = 2, .

    L(m, n), m 2, - 000, m00, 0m0, 00m, mm00, , mmm, r(v, u) d0 = m, m 3 , . -, , - 000, 100, 010, 001, 1100, , 111, m00, 0m0, 00m, mm00, , mmm; , , m 2 : , ,, .

    L(m, n) L(m+k, n) L(m+k, n+t), k, t 1, , L(m, n), L(m+k, n) L(m+k, n+t).

    2. L-

    . 1 L- - -. . L(m, n) = 1ni, l(i) = m,

    -, , L(m, n) L(m, n), L(m, n) = L(m, n) -.

    . . L(m, n) - , A = {0, 1, , m}, j, - j- , (v) v j-: j = (v), 0 j nm.

    . L(m, n), - , . 1. , -.

    h(1k Pi) = 1k h(Pi) l(1ki) = 1k l(i), . [1], - : ln(xy) = ln(x) + ln(y) . Ach(j) -, j- L = i=1ni ach(j) = |Ach(j)| = wj ( ).

    2. 0 j m n 2 Ach(j) j- L = i=1ni, l(i) = m,i = 1, , n,

    ach(j, i=1nCi) = t=0j ach(t, i=1n1Ci), wj(i=1nCi) = t=0j wt(i=1n1Ci).

  • 18 ..

    . A(n, m, d0) ( W l = n m + 1), - (v, w) d0 . Sh(r, z):={x: (x, z) r} r 0 z, z , , Int(Sh(r, z)):= {x: (x, z) < r, r 1}, Sf(r, z):= Sh(r, z) \ Int(Sh(r, z)) = {x: (x, z) = r} Vsh(r, z):=Sh(r, z) .

    Vsh(r, z) =Sf(r, z) Int(Sh(r, z))= Sf(r, z) + Int(Sh(r, z)) r 1. r = 0 , Sh(0, z) ,

    0., Sh(r, z) L(n, m) r 1 z

    2, 2 , , -, d0 2, r d0/2.

    - r, , (. . 1), Vshmin(r), Vshmax(r) Vshsr(r) .

    mn/ Vshmax(r) mn/ Vshsr mn/ Vshmin, (m+1)n / Vshmax(r) maxA(n,m,d0) (m+1)n /d0. m + 1 A = {0, , m} , , 25:2 = 13.

    A = {0, 1}, m = 1, 2n / Vshmax(r) maxA(n, m, d0) 2n / d0.

    , maxA(n, m, d0) mn / Vshmax(r), 1+ mn / Vshmax(r), 2+ mn / Vshmax(r),, mn / d0.

    , - r, , , - maxA(n, m, d0) = mn:d0, mn:d0 . maxA(2, 5, 2)=13 d0=2, : 00, 11, 02, 20, 22, 13, 31, 33, 04, 40, 24, 42, 44, {0, 1, 2, 3, 4}, r = 1; maxA(n, m, d0)= mn:d0 n = 2, m = 5 d0 = 2.

    H- - n , , , , c r 0 r < n.

    L(n, m) H-, r , r , r

    Sf(r, z) = Cnr mr, Vsh(r, z) =1+ ri=1rCnri mri., H- m = 1 r

    2n / (1+ ri=1rCnri) maxA(n, m, d0) 2n / d0.

    L(m,n) 0 nm . [10, .1, .2], n n1 + n2 ++ nk - ( , , 1+2 = 2+1) - D(n) - . , , , 1+2 2+1, D(n) n (. D(5) D(5) . 2).

    1.1. D(n) [3, 5, 11].2. D(n) , : D(n) Bool(n1).3. n1 + n2 ++ nk D(n) D(n), -

    n1 + n2 ++ nk , - k- D(n) k- D(n),0 k n.

    sur(D(n)) = D(n). J D(n):D(n)= n J. D(n) n -

    A = {0, , n}: n + k n, 0 < , L(m, n+k) - D(i), 1 i n. - n+k- n L(m, n+k) D(n).

    , L- - , , , D(n) , D(n), , - (. . 2).

  • , 19

    (5)D

    (5)

    )2+3 ()3+2 ()1+4 ()4+1 (

    )+22+1) (+21+2) (+12+2) (1+1+3()1+3+1()3+1+1(

    )1+1+1+2()1+1+2+1()1+2+1+1 ()2+1+1+1(

    )1+1+1+1+1(

    (5)D

    (5)

    )2+3) (1+4(

    )1+2+2 ()1+1+3(

    )1+1+1+2(

    1+1+1+1+1)(

    . 2

    D(n) Bool(n1) 111, 211, , 112,, n11, n n 1 {1, , n} - n1 {0, 1}, . D(n) D(n + k), k = 1, , : D(n + k) D(n) () , ..; , , L(m, n) L(m+k, n) L(m+k, n+t), k, t 1, L(m, n). , (, ).

    3. : -

    S [10, 11], A S p, q S .

    [10, . II, 3, 2.29 ( )], T = {p: pL} - L : ' ' = {p: p sup(T' ), pT, ' } .

    , 1 . 2. T - A = {0, 1}

    . T o : T{o} , - T{o}, ( . [12, 13]).

    [2]. - C L c-, ' , ' , c1, c2 C :

    c1 (') c1 ('c2) c2, o < c2 c2 c2 ('c1). 1, - LA -, -

    , -, . - 25- [14]:

    , a = ( )1n a

    iiLa

    =

    , Lai , - ( ), . [2].

    .

    , , , - , , s-, .

    , , . , ( ), , [15]. - . ( - , , ) , - ML- p- [2, 3].

    , ,. [16 18], , .

    , s- . [7, 19, 20].

    [8, 9], . [1, 3 5, 10].

  • 20 ..

    1. .. // . . 2006. 17. . 30 34. 2. .. P- // . 2005. . 17. . 3. . 146 160. 3. .. // . :- , 2001. . 90 103.

    4. .. . I // .: - , 2001. . 74 91.

    5. .. , , . III // : . .-. .: . : - , 2000. . 74 79.

    6. .. // . .: ,2001. 4. . 79 84.

    7. .. . II // . : - ,1998. . 73 81.

    8. ., . , . . 1. .: , 1990. 9. - .., ... , . .: , 1979. 10. M. . M.: , 1982. 558 . 11. . . .: , 1984. 12. .., .., .. , , . .: , 1981. 13. .. . : - , 1987. 14. .. . .: , 1961. 15. .. . : , 1999. 16. .. . : - . -, 1993. 17. .., .. . .: , 1997. 18. .. // . . 1992. 17.. 33 36.

    19. .. : // . -. 2003. 30. . 14 27.

    20. .. s- // . 2001. . 26. . 117 126.