MinT - Information on Result #1183360

Information on Result #1183360

Digital (162, 172, 5034014)-net over F₃, using net defined by OOA based on linear OOA(3¹⁷², 5034014, F₃, 15, 10) (dual of [(5034014, 15), 75510038, 11]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(3¹⁷², 5034015, F₃, 5, 10) (dual of [(5034015, 5), 25169903, 11]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3²⁰, 1678005, F₃, 5, 3) (dual of [(1678005, 5), 8390005, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3²⁰, 3713024, F₃, 5, 3) (dual of [(3713024, 5), 18565100, 4]-NRT-code), using
      - appending 2 arbitrary columns [i] based on linear OOA(3²⁰, 3713024, F₃, 3, 3) (dual of [(3713024, 3), 11139052, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(3²⁰, 3713024, F₃, 2, 3) (dual of [(3713024, 2), 7426028, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3²⁰, 3713024, F₃, 3) (dual of [3713024, 3713004, 4]-code or 3713024-cap in PG(19,3)), using
        large caps in PG(u,Â 3) [i]
  2. linear OOA(3⁴³, 1678005, F₃, 5, 5) (dual of [(1678005, 5), 8389982, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁴³, 2391491, F₃, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴³, 4782983, F₃, 5) (dual of [4782983, 4782940, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(3⁴³, 4782969, F₃, 5) (dual of [4782969, 4782926, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(3²⁹, 4782969, F₃, 4) (dual of [4782969, 4782940, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(3⁰, 14, F₃, 0) (dual of [14, 14, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
  3. linear OOA(3¹⁰⁹, 1678005, F₃, 5, 10) (dual of [(1678005, 5), 8389916, 11]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(3¹⁸, 285, F₃, 5, 5) (dual of [(285, 5), 1407, 6]-NRT-code), using
        appending kth column [i] based on linear OOA(3¹⁸, 285, F₃, 4, 5) (dual of [(285, 4), 1122, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(3¹, 95, F₃, 4, 1) (dual of [(95, 4), 379, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 4, 1) for arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OOA(3⁵, 95, F₃, 4, 2) (dual of [(95, 4), 375, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(3⁵, 121, F₃, 4, 2) (dual of [(121, 4), 479, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(3⁵, 121, F₃, 2, 2) (dual of [(121, 2), 237, 3]-NRT-code), using
        appending kth column [i] based on linear OA(3⁵, 121, F₃, 2) (dual of [121, 116, 3]-code), using
        Hamming code H(5,3) [i]
        linear OOA(3¹², 95, F₃, 4, 5) (dual of [(95, 4), 368, 6]-NRT-code), using
        extracting embedded OOA [i] based on digital (7, 12, 95)-net over F₃, using
        linear code embedding found in a computer search [i]
      2. linear OOA(3⁹¹, 1677720, F₃, 5, 10) (dual of [(1677720, 5), 8388509, 11]-NRT-code), using
        OOA 5-folding [i] based on linear OA(3⁹¹, 8388600, F₃, 10) (dual of [8388600, 8388509, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁹¹, large, F₃, 10) (dual of [large, large−91, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.