MinT - Information on Result #1716799

Information on Result #1716799

Linear OOA(3²⁰⁵, 1225, F₃, 45, 36) (dual of [(1225, 45), 54920, 37]-NRT-code), using OOA 4-folding and stacking with additional row based on linear OOA(3²⁰⁵, 4901, F₃, 5, 36) (dual of [(4901, 5), 24300, 37]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁰⁵, 4901, F₃, 36) (dual of [4901, 4696, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3²⁰⁵, 6606, F₃, 36) (dual of [6606, 6401, 37]-code), using
  - strength reduction [i] based on linear OA(3²⁰⁵, 6606, F₃, 37) (dual of [6606, 6401, 38]-code), using
    - constructionÂ X applied to C([0,18]) âŠ‚ C([0,15]) [i] based on
      1. linear OA(3¹⁹³, 6562, F₃, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
      2. linear OA(3¹⁶¹, 6562, F₃, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
      3. linear OA(3¹², 44, F₃, 5) (dual of [44, 32, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹², 54, F₃, 5) (dual of [54, 42, 6]-code), using
        (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
        linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code 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 OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
        linear OA(3⁸, 28, F₃, 5) (dual of [28, 20, 6]-code), using
        dual code (with bound on d by constructionÂ Y1) [i] based on
        linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
        contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
        nonexistence of linear OA(3¹⁹, 23, F₃, 14) (dual of [23, 4, 15]-code), because
        2 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]

Mode: Linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (169, 205, 1225)-net over F₃	[i]		Net Defined by OOA