MinT - Information on Result #1117777

Information on Result #1117777

Linear OOA(3²³⁰, 1679364, F₃, 5, 18) (dual of [(1679364, 5), 8396590, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵⁰, 1644, F₃, 5, 9) (dual of [(1644, 5), 8170, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3⁵⁰, 6577, F₃, 9) (dual of [6577, 6527, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁵⁰, 6579, F₃, 9) (dual of [6579, 6529, 10]-code), using
    - constructionÂ X applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
      1. linear OA(3⁴⁹, 6562, F₃, 9) (dual of [6562, 6513, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
      2. linear OA(3³³, 6562, F₃, 7) (dual of [6562, 6529, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      3. linear OA(3¹, 17, F₃, 1) (dual of [17, 16, 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(3¹⁸⁰, 1677720, F₃, 5, 18) (dual of [(1677720, 5), 8388420, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁸⁰, 8388600, F₃, 18) (dual of [8388600, 8388420, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.