MinT - Information on Result #1117514

Information on Result #1117514

Linear OOA(3¹⁶⁶, 1678451, F₃, 5, 14) (dual of [(1678451, 5), 8392089, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁰, 731, F₃, 5, 7) (dual of [(731, 5), 3625, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3³⁰, 2194, F₃, 7) (dual of [2194, 2164, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(3³⁰, 2195, F₃, 7) (dual of [2195, 2165, 8]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(4) [i] based on
      1. linear OA(3²⁹, 2187, F₃, 7) (dual of [2187, 2158, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(3²², 2187, F₃, 5) (dual of [2187, 2165, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      3. linear OA(3¹, 8, F₃, 1) (dual of [8, 7, 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 OOA(3¹³⁶, 1677720, F₃, 5, 14) (dual of [(1677720, 5), 8388464, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹³⁶, 8388600, F₃, 14) (dual of [8388600, 8388464, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹³⁶, large, F₃, 14) (dual of [large, large−136, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.

Other Results with Identical Parameters

None.

Depending Results

None.