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Improved lower bounds for self-dual codes over F11, F13, F17, F19 and F23

  • *Corresponding author: Masaaki Harada

    *Corresponding author: Masaaki Harada

The second author is supported by JSPS KAKENHI Grant Number 19H01802

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  • We construct self-dual codes over F11, F13, F17, F19 and F23 which improve the previously known lower bounds on the largest minimum weights. In particular, the largest possible minimum weight among self-dual [n,n/2] codes over Fp is determined for (p,n)=(19,24) and (23,28).

    Mathematics Subject Classification: Primary: 94B05; Secondary: 94B25.

    Citation:

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  • Table 1.  New four-negacirculant self-dual codes Cp,n,d

    p n d rA rB
    11 24 10 (1,3,8,0,9,7) (3,5,2,8,0,1)
    11 28 11 (1,5,9,4,0,4,2) (1,4,10,0,0,7,3)
    13 28 12 (1,10,8,7,3,9,11) (2,6,10,3,7,11,10)
    13 32 13 (1,3,7,3,4,12,2,8) (5,11,7,2,4,3,4,3)
    13 36 14 (1,11,11,10,9,5,12,3,6) (9,7,11,4,9,10,12,0,2)
    13 40 15 (1,4,3,6,3,12,12,9,7,11) (11,0,0,8,7,4,5,8,10,4)
    17 24 11 (1,5,8,11,7,7) (5,12,5,12,4,4)
    17 28 12 (1,10,6,13,2,2,16) (16,15,1,3,14,14,5)
    17 32 13 (1,6,3,7,15,16,14,5) (15,13,3,12,9,6,8,15)
    17 36 14 (1,10,8,10,3,2,4,1,7) (0,0,8,11,3,8,3,10,11)
    17 40 15 (1,5,9,2,9,16,14,14,13,16) (7,0,11,0,5,12,4,12,2,13)
    19 24 12 (3,9,1,0,18,10) (7,10,4,3,11,5)
    19 28 12 (1,5,14,10,0,12,6) (15,14,1,4,9,14,6)
    23 28 14 (1,11,8,15,12,22,19) (22,16,15,21,15,16,22)
    23 32 13 (1,3,7,7,22,3,4,9) (5,2,4,22,13,7,6,17)
    23 36 15 (1,17,14,9,6,5,1,20,4) (8,15,19,6,18,3,20,19,16)
    23 40 16 (1,17,17,17,9,4,10,15,13,1) (19,20,4,16,10,22,4,21,16,21)
     | Show Table
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    Table 2.  New double circulant self-dual codes Cp,n,d

    p n d rA
    13 26 11 (0,0,11,9,10,11,3,9,9,7,2,1,1)
    13 30 12 (12,0,7,7,5,9,12,8,11,7,4,12,0,3,12)
    13 38 14 (4,0,9,9,4,2,9,3,8,9,8,9,10,0,4,8,0,2,11)
     | Show Table
    DownLoad: CSV

    Table 3.  New quasi-twisted self-dual codes Cp,n,d

    p n d rA
    13 34 13 (7,12,5,1,9,2,10,7,10,12,6,12,0,0,0,3,7)
    17 26 11 (1,14,9,10,8,1,12,16,0,10,2,0,15)
     | Show Table
    DownLoad: CSV

    Table 4.  Weight enumerators of self-dual [24,12,12] codes over F19

    i Ai
    0 1
    12 A12
    13 4493059212A12
    14 211815648+66A12
    15 4377523392220A12
    16 39503618352+495A12
    17 343122660144792A12
    18 2391276145104+924A12
    19 13601985566400792A12
    20 61202848135968+495A12
    21 209841090069600220A12
    22 515063659381920+66A12
    23 80618674966675212A12
    24 604640049552288+A12
     | Show Table
    DownLoad: CSV

    Table 5.  Weight enumerators of self-dual [28,14,14] codes over F23

    i Ai
    0 1
    14 A14
    15 82372752014A14
    16 5354228880+91A14
    17 132753380760364A14
    18 1623118737240+1001A14
    19 191556517152002002A14
    20 189055086620400+3003A14
    21 15851684365545603432A14
    22 11095536548416320+3003A14
    23 636791714731972802002A14
    24 291862645189315200+1001A14
    25 1027356593521514256364A14
    26 2607905178181294992+91A14
    27 424991955283216182414A14
    28 3339222505567885376+A14
     | Show Table
    DownLoad: CSV

    Table 6.  dp(n) (p{11,13,17,19,23},n{14,16,,40})

    np 11 13 17 19 23
    14 8 7–8
    16 8 8 8–9 8–9 9
    18 9 10
    20 10 10 10 11 10–11
    22 10–11 10–11
    24 10–12 10–12 11–12 12 13
    26 11–13 11–13
    28 11–14 12–14 12–14 12–14 14
    30 12–15 12–15
    32 12–16 13–16 13–16 14–16 13–16
    34 13–17 13–17
    36 13–18 14–18 14-18 14–18 15–18
    38 14–19 14–19
    40 14–20 15–20 15–20 15–20 16–20
     | Show Table
    DownLoad: CSV
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