MinT - Information on Result #1117723

Information on Result #1117723

Linear OOA(3¹⁹⁷, 1677903, F₃, 5, 17) (dual of [(1677903, 5), 8389318, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³¹, 183, F₃, 5, 8) (dual of [(183, 5), 884, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3³¹, 732, F₃, 8) (dual of [732, 701, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3³¹, 735, F₃, 8) (dual of [735, 704, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(3³¹, 729, F₃, 8) (dual of [729, 698, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(3²⁵, 729, F₃, 7) (dual of [729, 704, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(3⁰, 6, F₃, 0) (dual of [6, 6, 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]
linear OOA(3¹⁶⁶, 1677720, F₃, 5, 17) (dual of [(1677720, 5), 8388434, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁶⁶, 8388600, F₃, 17) (dual of [8388600, 8388434, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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.